It consists of six provinces, namely, Albay, Camarines Norte, Camarines Sur, Catanduanes, Masbate, and Sorsogon
Albay
capital is Legazpi City
Languages. Bicolano
Traditional industries. Agriculture is the main industry
crops as coconut, rice, sugar, and abaca.
Handicrafts is the major source of rural income.
Tourism, primarily because of Mayon Volcano,
Bicol's largest industrial sites are in Albay
Her name was derived from the Bikol word "Magayon" which means beautiful.
Friday, August 27, 2010
Wednesday, August 25, 2010
math poem 6
?
THE ARROW AND THE QUESTION
(with apologies to Henry Wadsworth Longfellow)
I shoot an arrow into the air
A projectile that it seemed it were
Daftary plotted its position
Scythian formed the required equation
Long, long afterward, under an oak
As I read a Mathematics book
There, by chance, I found a queer entry
Dragan K has asked the same query
So I logged on to Yahoo Answers
To post the question for web viewers
Dr D, Zo Maar starred the question
Half-Blood Prince, Falzoon gave attention
And so did Al P and Ergaster
Mathsmanretired, Civil Aviator
Mathematishan, Rakesh Dubey
And smart Queen Eti Wants Spaghetti
Bhaskar and Algol gave their answers
Tomato, Skonhet and all others
Though all were great, I'll choose an entry
Rozeta Fifty Three gets BA
You are late, good Dr. Lucafont
And First Grade Rocks, there's no more question
So sorry folks, it got deleted
It didn't conform to rules as posted.
* 5 months ago
Additional Details
For the record, I did not choose the category, it just got suggested by Yahoo.
5 months ago
You know, I dabbled on Poetry these last days.
5 months ago
Lovechild,
I didn't know that you also have some bearings in the realm of Quantum Mechanics...wow
5 months ago
I have to make this poem longer to include, Vikram P, Randy, Carulos, the Mathemagician, steve, Bandagadde S, Edward, Anil Bakshi, Otro, Evan, Quadrillerator, Mielo Estetz, Tabula Raza, and others in the Math and Physics....
5 months ago
Bhaskar, you don't have to take it literally. Seems your name has a good sound and the right number of syllables(lol) Nice day.
5 months ago
Madhukarji,
Don't you worry, we'll use radar tracking.
5 months ago
Scythian,
It will be a long-winding poem of quatrains like the "Centuries" of Nostradamus (lol)
5 months ago
♥5, how will people read your name in a poem.
5 months ago
Al P,
Welcome to Poetry section (lol)
When the math people all answer in poetry, who will be left to make equations?
5 months ago
Al P,
Keep on. Your spirit has a bearing in Poetry. Just think that Science don't clash with poetry, they're just alternate worlds for each other.
5 months ago
================================
The additional stanzas for the above poem:
This incident has kept me thinking
Why this has happened to my posting
It left no chance even for comments
Of other friends who missed the contents
Think I'll repost much better questions
Worth your while to see in this section
That everyone who'd chance to drop by
Gets impressed of norms that are so high
Check the page of these contributors
Steve, Vasek and Quadrillerator
Mathemagician and Vikram P
Mielo Estetz and Anil Bakshi
Tabula Raza, JB and Hy
Conan, Saket, and SMCI
A Kartaltepe, Otro, Moise Gunen
Northstar, Evan, Randy and Rackbrane
Euclid, Pythagoras and others
Might all rejoice to think, or shudder
In Math there'll be no more dilemma
We just resort to Wolfram Alpha
5 months ago
Sir Duke and Kirchwey, we should consult
For their opinions before we vote;
Edward, Gzion, Bandagadde S,
May then solve the problem if we please
5 months ago
Sir Duke and Kirchwey, we should consult
For their opinions before we vote;
Edward, Gzion, Bandagadde S,
May then solve the problem if we please
5 months ago
Old Pilot and love5 have replied
So did Retired Pilot who supplied
Answers, explanations where required;
There's Gianlino, whose queries I've tried.
Astronomy has got DLM,
Erica S, professor, a dame,
And Carolus, whose answers we see;
For Philosophy, there's Hector C.
THE ARROW AND THE QUESTION
(with apologies to Henry Wadsworth Longfellow)
I shoot an arrow into the air
A projectile that it seemed it were
Daftary plotted its position
Scythian formed the required equation
Long, long afterward, under an oak
As I read a Mathematics book
There, by chance, I found a queer entry
Dragan K has asked the same query
So I logged on to Yahoo Answers
To post the question for web viewers
Dr D, Zo Maar starred the question
Half-Blood Prince, Falzoon gave attention
And so did Al P and Ergaster
Mathsmanretired, Civil Aviator
Mathematishan, Rakesh Dubey
And smart Queen Eti Wants Spaghetti
Bhaskar and Algol gave their answers
Tomato, Skonhet and all others
Though all were great, I'll choose an entry
Rozeta Fifty Three gets BA
You are late, good Dr. Lucafont
And First Grade Rocks, there's no more question
So sorry folks, it got deleted
It didn't conform to rules as posted.
* 5 months ago
Additional Details
For the record, I did not choose the category, it just got suggested by Yahoo.
5 months ago
You know, I dabbled on Poetry these last days.
5 months ago
Lovechild,
I didn't know that you also have some bearings in the realm of Quantum Mechanics...wow
5 months ago
I have to make this poem longer to include, Vikram P, Randy, Carulos, the Mathemagician, steve, Bandagadde S, Edward, Anil Bakshi, Otro, Evan, Quadrillerator, Mielo Estetz, Tabula Raza, and others in the Math and Physics....
5 months ago
Bhaskar, you don't have to take it literally. Seems your name has a good sound and the right number of syllables(lol) Nice day.
5 months ago
Madhukarji,
Don't you worry, we'll use radar tracking.
5 months ago
Scythian,
It will be a long-winding poem of quatrains like the "Centuries" of Nostradamus (lol)
5 months ago
♥5, how will people read your name in a poem.
5 months ago
Al P,
Welcome to Poetry section (lol)
When the math people all answer in poetry, who will be left to make equations?
5 months ago
Al P,
Keep on. Your spirit has a bearing in Poetry. Just think that Science don't clash with poetry, they're just alternate worlds for each other.
5 months ago
================================
The additional stanzas for the above poem:
This incident has kept me thinking
Why this has happened to my posting
It left no chance even for comments
Of other friends who missed the contents
Think I'll repost much better questions
Worth your while to see in this section
That everyone who'd chance to drop by
Gets impressed of norms that are so high
Check the page of these contributors
Steve, Vasek and Quadrillerator
Mathemagician and Vikram P
Mielo Estetz and Anil Bakshi
Tabula Raza, JB and Hy
Conan, Saket, and SMCI
A Kartaltepe, Otro, Moise Gunen
Northstar, Evan, Randy and Rackbrane
Euclid, Pythagoras and others
Might all rejoice to think, or shudder
In Math there'll be no more dilemma
We just resort to Wolfram Alpha
5 months ago
Sir Duke and Kirchwey, we should consult
For their opinions before we vote;
Edward, Gzion, Bandagadde S,
May then solve the problem if we please
5 months ago
Sir Duke and Kirchwey, we should consult
For their opinions before we vote;
Edward, Gzion, Bandagadde S,
May then solve the problem if we please
5 months ago
Old Pilot and love5 have replied
So did Retired Pilot who supplied
Answers, explanations where required;
There's Gianlino, whose queries I've tried.
Astronomy has got DLM,
Erica S, professor, a dame,
And Carolus, whose answers we see;
For Philosophy, there's Hector C.
math poems 5
s
Math Quotes
These page contains quotations on Mathematics by famous mathematicians.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. ~John Louis von Neumann
Pure mathematics is, in its way, the poetry of logical ideas. ~Albert Einstein
Mathematics are well and good but nature keeps dragging us around by the nose. ~Albert Einstein
Black holes result from God dividing the universe by zero. ~Author Unknown
Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs. ~Isaac Barrow
I never did very well in math - I could never seem to persuade the teacher that I hadn't meant my answers literally. ~Calvin Trillin
Math is radical! ~Bumper Sticker
If you think dogs can't count, try putting three dog biscuits in your pocket and then giving Fido only two of them. ~Phil Pastoret
There was a blithe certainty that came from first comprehending the full Einstein field equations, arabesques of Greek letters clinging tenuously to the page, a gossamer web. They seemed insubstantial when you first saw them, a string of squiggles. Yet to follow the delicate tensors as they contracted, as the superscripts paired with subscripts, collapsing mathematically into concrete classical entities - potential; mass; forces vectoring in a curved geometry - that was a sublime experience. The iron fist of the real, inside the velvet glove of airy mathematics. ~Gregory Benford, Timescape
It is a mathematical fact that fifty percent of all doctors graduate in the bottom half of their class. ~Author Unknown
If two wrongs don't make a right, try three. ~Author Unknown
Arithmetic is where numbers fly like pigeons in and out of your head. ~Carl Sandburg, "Arithmetic"
Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer. ~Carl Sandburg, "Arithmetic"
If equations are trains threading the landscape of numbers, then no train stops at pi. ~Richard Preston
Even stranger things have happened; and perhaps the strangest of all is the marvel that mathematics should be possible to a race akin to the apes. ~Eric T. Bell, The Development of Mathematics
So if a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again. ~Francis Bacon, "Of Studies"
The essence of mathematics is not to make simple things complicated, but to make complicated things simple. ~S. Gudder
The human mind has never invented a labor-saving machine equal to algebra. ~Author Unknown
The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede. ~Edward Gibbon, Decline and Fall of the Roman Empire
Go down deep enough into anything and you will find mathematics. ~Dean Schlicter
It is not the job of mathematicians... to do correct arithmetical operations. It is the job of bank accountants. ~Samuil Shchatunovski
Trigonometry is a sine of the times. ~Author Unknown
Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere. ~W.S. Anglin
A mathematician is a device for turning coffee into theorems. ~Paul Erdos
The mathematics are usually considered as being the very antipodes of Poesy. Yet Mathesis and Poesy are of the closest kindred, for they are both works of the imagination. ~Thomas Hill
I used to love mathematics for its own sake, and I still do, because it allows for no hypocrisy and no vagueness.... ~Stendhal (Henri Beyle), The Life of Henri Brulard
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. ~Albert Einstein, Sidelights on Relativity
God does not care about our mathematical difficulties; He integrates empirically. ~Albert Einstein
If there is a God, he's a great mathematician. ~Paul Dirac
To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology. ~Hilda Phoebe Hudson
[T]he different branches of Arithmetic - Ambition, Distraction, Uglification, and Derision. ~Lewis Carroll
[G]eometry is not true, it is advantageous. ~Henri Poincaré
Infinity is a floorless room without walls or ceiling. ~Author Unknown
Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover. ~Bertrand Russell
If a healthy minded person takes an interest in science, he gets busy with his mathematics and haunts the laboratory. ~W.S. Franklin
Proof is an idol before whom the pure mathematician tortures himself. ~Arthur Stanley Eddington, The Nature of the Physical World
There was a young man from Trinity,
Who solved the square root of infinity.
While counting the digits,
He was seized by the fidgets,
Dropped science, and took up divinity.
~Author Unknown
One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers... ~Heinrich Hertz
In the binary system we count on our fists instead of on our fingers. ~Author Unknown
The laws of nature are but the mathematical thoughts of God. ~Euclid
In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generations adds a new story to the old structure. ~Hermann Hankel
Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too. ~Fyodor Mikhailovich Dostoevsky
I know that two and two make four - & should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 & 2 into five it would give me much greater pleasure. ~George Gordon, Lord Byron
Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting. ~Ernst Mach
Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding. ~Percy William Bridgman, The Way Things Are
Why do we believe that in all matters the odd numbers are more powerful? ~Pliny the Elder, Natural History
Uneven numbers are the gods' delight. ~Virgil, The Eclogues
One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories. ~Philip J. Davis
Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub. ~Richard J. Trudeau, Dots and Lines
I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because like Spinoza's God, it won't love us in return. ~Bertrand Russell, 1912
The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization. ~John Kemeny
Although I am almost illiterate mathematically, I grasped very early in life that any one who can count to ten can count upward indefinitely if he is fool enough to do so. ~Robertson Davies, "Of the Conservation of Youth," The Table Talk of Samuel Marchbanks
Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings. ~Alfred North Whitehead
The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, "refuge from the goading urgency of contingent happenings," and the sort of beauty changeless mountains present to sense tried by the present-day kaleidoscope of events. ~Morris Kline, Mathematics in Western Culture (Kline is quoting Alfred North Whitehead - "refuge from...")
Mathematics is as much an aspect of culture as it is a collection of algorithms. ~Carl Boyer, 1949, calculus textbook
The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry. ~Eric Bell, The Search for Truth
Sometimes it is useful to know how large your zero is. ~Author Unknown
The hardest arithmetic to master is that which enables us to count our blessings. ~Eric Hoffer, Reflections On The Human Condition
Mathematics is the only good metaphysics. ~William Thomson Baron Kelvin of Largs
The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic. ~Bertrand Russell
Music is the pleasure the human mind experiences from counting without being aware that it is counting. ~Gottfried Leibniz
How many times can you subtract 7 from 83, and what is left afterwards? You can subtract it as many times as you want, and it leaves 76 every time. ~Author Unknown
To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas. ~Ivars Peterson
With my full philosophical rucksack I can only climb slowly up the mountain of mathematics. ~Ludwig Wittgenstein, Culture and Value
But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius. ~Harold Marston Morse
Still more astonishing is that world of rigorous fantasy we call mathematics. ~Gregory Bateson
Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house. ~Robert Heinlein, Time Enough for Love
The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions. ~Ronald L. Graham
We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years. ~Mark Twain
Can you do Division? Divide a loaf by a knife - what's the answer to that? ~Lewis Carroll, Through the Looking Glass
Mathematics is the supreme judge; from its decisions there is no appeal. ~Tobias Dantzig
Although he may not always recognize his bondage, modern man lives under a tyranny of numbers. ~Nicholas Eberstadt, The Tyranny of Numbers: Mismeasurement and Misrule
A man has one hundred dollars and you leave him with two dollars. That's subtraction. ~Mae West
I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation.... ~Paul Auster, The Music of Chance
Math Quotes
These page contains quotations on Mathematics by famous mathematicians.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. ~John Louis von Neumann
Pure mathematics is, in its way, the poetry of logical ideas. ~Albert Einstein
Mathematics are well and good but nature keeps dragging us around by the nose. ~Albert Einstein
Black holes result from God dividing the universe by zero. ~Author Unknown
Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs. ~Isaac Barrow
I never did very well in math - I could never seem to persuade the teacher that I hadn't meant my answers literally. ~Calvin Trillin
Math is radical! ~Bumper Sticker
If you think dogs can't count, try putting three dog biscuits in your pocket and then giving Fido only two of them. ~Phil Pastoret
There was a blithe certainty that came from first comprehending the full Einstein field equations, arabesques of Greek letters clinging tenuously to the page, a gossamer web. They seemed insubstantial when you first saw them, a string of squiggles. Yet to follow the delicate tensors as they contracted, as the superscripts paired with subscripts, collapsing mathematically into concrete classical entities - potential; mass; forces vectoring in a curved geometry - that was a sublime experience. The iron fist of the real, inside the velvet glove of airy mathematics. ~Gregory Benford, Timescape
It is a mathematical fact that fifty percent of all doctors graduate in the bottom half of their class. ~Author Unknown
If two wrongs don't make a right, try three. ~Author Unknown
Arithmetic is where numbers fly like pigeons in and out of your head. ~Carl Sandburg, "Arithmetic"
Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer. ~Carl Sandburg, "Arithmetic"
If equations are trains threading the landscape of numbers, then no train stops at pi. ~Richard Preston
Even stranger things have happened; and perhaps the strangest of all is the marvel that mathematics should be possible to a race akin to the apes. ~Eric T. Bell, The Development of Mathematics
So if a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again. ~Francis Bacon, "Of Studies"
The essence of mathematics is not to make simple things complicated, but to make complicated things simple. ~S. Gudder
The human mind has never invented a labor-saving machine equal to algebra. ~Author Unknown
The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede. ~Edward Gibbon, Decline and Fall of the Roman Empire
Go down deep enough into anything and you will find mathematics. ~Dean Schlicter
It is not the job of mathematicians... to do correct arithmetical operations. It is the job of bank accountants. ~Samuil Shchatunovski
Trigonometry is a sine of the times. ~Author Unknown
Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere. ~W.S. Anglin
A mathematician is a device for turning coffee into theorems. ~Paul Erdos
The mathematics are usually considered as being the very antipodes of Poesy. Yet Mathesis and Poesy are of the closest kindred, for they are both works of the imagination. ~Thomas Hill
I used to love mathematics for its own sake, and I still do, because it allows for no hypocrisy and no vagueness.... ~Stendhal (Henri Beyle), The Life of Henri Brulard
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. ~Albert Einstein, Sidelights on Relativity
God does not care about our mathematical difficulties; He integrates empirically. ~Albert Einstein
If there is a God, he's a great mathematician. ~Paul Dirac
To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology. ~Hilda Phoebe Hudson
[T]he different branches of Arithmetic - Ambition, Distraction, Uglification, and Derision. ~Lewis Carroll
[G]eometry is not true, it is advantageous. ~Henri Poincaré
Infinity is a floorless room without walls or ceiling. ~Author Unknown
Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover. ~Bertrand Russell
If a healthy minded person takes an interest in science, he gets busy with his mathematics and haunts the laboratory. ~W.S. Franklin
Proof is an idol before whom the pure mathematician tortures himself. ~Arthur Stanley Eddington, The Nature of the Physical World
There was a young man from Trinity,
Who solved the square root of infinity.
While counting the digits,
He was seized by the fidgets,
Dropped science, and took up divinity.
~Author Unknown
One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers... ~Heinrich Hertz
In the binary system we count on our fists instead of on our fingers. ~Author Unknown
The laws of nature are but the mathematical thoughts of God. ~Euclid
In most sciences one generation tears down what another has built and what one has established another undoes. In mathematics alone each generations adds a new story to the old structure. ~Hermann Hankel
Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too. ~Fyodor Mikhailovich Dostoevsky
I know that two and two make four - & should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 & 2 into five it would give me much greater pleasure. ~George Gordon, Lord Byron
Mathematics may be defined as the economy of counting. There is no problem in the whole of mathematics which cannot be solved by direct counting. ~Ernst Mach
Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding. ~Percy William Bridgman, The Way Things Are
Why do we believe that in all matters the odd numbers are more powerful? ~Pliny the Elder, Natural History
Uneven numbers are the gods' delight. ~Virgil, The Eclogues
One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories. ~Philip J. Davis
Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub. ~Richard J. Trudeau, Dots and Lines
I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because like Spinoza's God, it won't love us in return. ~Bertrand Russell, 1912
The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization. ~John Kemeny
Although I am almost illiterate mathematically, I grasped very early in life that any one who can count to ten can count upward indefinitely if he is fool enough to do so. ~Robertson Davies, "Of the Conservation of Youth," The Table Talk of Samuel Marchbanks
Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings. ~Alfred North Whitehead
The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, "refuge from the goading urgency of contingent happenings," and the sort of beauty changeless mountains present to sense tried by the present-day kaleidoscope of events. ~Morris Kline, Mathematics in Western Culture (Kline is quoting Alfred North Whitehead - "refuge from...")
Mathematics is as much an aspect of culture as it is a collection of algorithms. ~Carl Boyer, 1949, calculus textbook
The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry. ~Eric Bell, The Search for Truth
Sometimes it is useful to know how large your zero is. ~Author Unknown
The hardest arithmetic to master is that which enables us to count our blessings. ~Eric Hoffer, Reflections On The Human Condition
Mathematics is the only good metaphysics. ~William Thomson Baron Kelvin of Largs
The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic. ~Bertrand Russell
Music is the pleasure the human mind experiences from counting without being aware that it is counting. ~Gottfried Leibniz
How many times can you subtract 7 from 83, and what is left afterwards? You can subtract it as many times as you want, and it leaves 76 every time. ~Author Unknown
To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas. ~Ivars Peterson
With my full philosophical rucksack I can only climb slowly up the mountain of mathematics. ~Ludwig Wittgenstein, Culture and Value
But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius. ~Harold Marston Morse
Still more astonishing is that world of rigorous fantasy we call mathematics. ~Gregory Bateson
Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house. ~Robert Heinlein, Time Enough for Love
The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can't even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions. ~Ronald L. Graham
We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years. ~Mark Twain
Can you do Division? Divide a loaf by a knife - what's the answer to that? ~Lewis Carroll, Through the Looking Glass
Mathematics is the supreme judge; from its decisions there is no appeal. ~Tobias Dantzig
Although he may not always recognize his bondage, modern man lives under a tyranny of numbers. ~Nicholas Eberstadt, The Tyranny of Numbers: Mismeasurement and Misrule
A man has one hundred dollars and you leave him with two dollars. That's subtraction. ~Mae West
I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation.... ~Paul Auster, The Music of Chance
math poems 4
Math Poems
These poems had been written by Eileen Tupaz.
Odd - Even Poem
Zero, two, four, six, eight
Being even is just great.
One, three, five, seven, nine
Being odd is just fine.
Zero the hero came to school.
Zero the hero knows a rule:
Zero the hero stays in a space,
So all the other numbers get in the right place!
We sing a song to the tune of "Frere Jacques":
Zero Hero, Zero Hero,
We love you.
We love you.
Though you may be nothing,
We really think you're something.
Yes, we do. Yes, we do.
CLOCK SONG
(tune Wheels on the Bus)
The hands on the clock go round and round,
Round and round, round and round.
The hands on the clock go round and round.
To tell us the time.
The short hand on the clock
Goes from number to number,
Number to number, number to number.
The short hand on the clock
Goes from number to number.
To tell us the time.
The long hand on the clock
Goes around by fives,
Around by fives, around by fives.
The long hand on the clock
Goes around by fives.
To tell us the minutes.
The Skip Count Song
(Tune: Skip to my Lou)
Skip count, skip count, count by 2's
Skip count, skip count, count by 2's
Skip count, skip count, count by 2's
We can count to 20.
2, 4, 6, 8, 10,12,14,16, 18, 20 (chant this line)
Skip count, skip count, count by 5's
Skip count, skip count, count by 5's
Skip count, skip count, count by 5's
We can count to 50.
5, 10, 15, 20, (up to 50)
Skip count, skip count, count by 10's
Skip count, skip count, count by 10's
Skip count, skip count, count by 10's
We can count to 100.
10, 20, 30, 40, (up to 100)
Shelby Star is my name
Shining brightly is my game
With five sparkly points and lots of sides, too
With wishes I make dreams come true.
I am Cindi Circle
Watch me turn
Round and round
And you will learn
I'm not straight and
I don't bend
My outside edges
Never end!
Sammy Square is my name
My four sides are just the same
Turn me around, I don't care
I'm always the same, I'm a square!
I am Danny Diamond
I am like a kite
But I'm really just a square
Whose corners are pulled tight
Ricky rectangle is my name
My four sides are not the same
Two are short and two are long
Count my sides, come along
1-2-3-4
Tommy Triangle is the name for me
Count my sides - there's 1-2-3
I am Ollie Oval
A football shape is mine
Some people think that I"m an egg
But I think I look fine!
OR
Opal Oval is my name.
The circle and I are not the same.
The circle is round, as round can be.
I am shaped like an egg as you can see
Harry Heart is my name
The shape I make is my fame
With a point on the bottom and two humps on top
When it comes to love I just can't stop!
1 A straight line down and 1 is done.
2 Around and back on the railroad track, 2,2,2.
(Read as "choo-choo-choo")
3 Go around and around a tree. That's the way to write a 3.
4 Down and across and down once more. That's way to write 4.
5 Down and around, make it fat. Numeral 5 wears a hat.
6 Down and around, make a loop. Numeral 6 rolls a hoop.
7 Across, slant, then you are done. Writing 7 can be fun.
8 Write an S but do not wait. Come back up and write an 8.
9 A loop and a line make numeral 9.
10 Pull down straight, lift, and then curve down, curve up--that's a 10.
Number Poem
Down you run and 1 is done.
Around, and down, and out go you,
That's the way to make a 2.
Around, and around, like a bee,
That's the way to make a 3.
Down, across, and down once more,
That's the way to make a 4.
Short neck, belly fat,
Number 5 wears a hat.
Down, around, in a circle you go,
That's a six, just as you know.
Straight across, slide down from heaven,
That's the way to make a 7.
First a snake, then come back straight,
That's the way to make an 8.
First a ball and then a line,
That's the way to make a 9.
Tall straight, circle then,
That's the way to make a 10
Circumference and Area
Fiddle de dum, Fiddle de dee,
A ring round the moon is pi times d;
But if a hole you want repaired,
You use the formula Pi r squared.
A New Solution to an Old Problem
By: Eleanor Ninestein
The Topologist's child was quite hyper
'Til she wore a Moebius diaper.
The mess on the inside
Was thus on the outside
And it was easy for someone to wipe her.
The Mobius Strip
A mathematician confided
That a Mobius band is one-sided.
And you'll get quite a laugh
If you cut it in half,
For it stays in one piece when divided.
Einstein
By: Katherine O'Brien
The Mathematics Teacher
April 1968
His first day at Princeton, the legend goes,
he went for a stroll (in his rumpled clothes).
He entered a coffee shop -- moment of doubt --
then climbed on a stool and looked about.
Beside him, a frosh, likewise strange and alone,
consoling himself with an ice cream cone.
Now Einstein's glee
was plain to see
at the sight of the cone with the sphere on top
(in the hand of a frosh in a sandwich shop)
and -- oh incredible --
completely edible!
He smiled at the frosh, then the waiter came,
and Einstein gestured he'd like the same, and they sat there nibbling, suddenly kin,
with no common language to verbalize in.
But foreign no longer, no longer alone,
with the fellowship bond of an ice cream cone.
Valentine
You disintegrate my differential,
You dislocate my focus.
My pulse goes up like an exponential
whenever you cross my locus.
Without you, sets are null and void --
so won't you be my cardioid?
Threes
By: John Atherton
I think that I shall never c
A # lovelier than 3;
For 3 < 6 or 4,
And than 1 it's slightly more.
All things in nature come in 3s,
Like ... , trio's, Q.E.D.s;
While $s gain more dignity
if augmented 3 x 3 --
A 3 whose slender curves are pressed
By banks, for compound interest;
Oh, would that, paying loans or rent,
My rates were only 3%!
3² expands with rapture free,
And reaches toward infinity;
3 complements each x and y,
And intimately lives with pi.
A circle's # of °
Are best ÷ up by 3s,
But wrapped in dim obscurity
Is the square root of 3.
Atoms are split by men like me,
But only God is 1 in 3.
These poems had been written by Eileen Tupaz.
Odd - Even Poem
Zero, two, four, six, eight
Being even is just great.
One, three, five, seven, nine
Being odd is just fine.
Zero the hero came to school.
Zero the hero knows a rule:
Zero the hero stays in a space,
So all the other numbers get in the right place!
We sing a song to the tune of "Frere Jacques":
Zero Hero, Zero Hero,
We love you.
We love you.
Though you may be nothing,
We really think you're something.
Yes, we do. Yes, we do.
CLOCK SONG
(tune Wheels on the Bus)
The hands on the clock go round and round,
Round and round, round and round.
The hands on the clock go round and round.
To tell us the time.
The short hand on the clock
Goes from number to number,
Number to number, number to number.
The short hand on the clock
Goes from number to number.
To tell us the time.
The long hand on the clock
Goes around by fives,
Around by fives, around by fives.
The long hand on the clock
Goes around by fives.
To tell us the minutes.
The Skip Count Song
(Tune: Skip to my Lou)
Skip count, skip count, count by 2's
Skip count, skip count, count by 2's
Skip count, skip count, count by 2's
We can count to 20.
2, 4, 6, 8, 10,12,14,16, 18, 20 (chant this line)
Skip count, skip count, count by 5's
Skip count, skip count, count by 5's
Skip count, skip count, count by 5's
We can count to 50.
5, 10, 15, 20, (up to 50)
Skip count, skip count, count by 10's
Skip count, skip count, count by 10's
Skip count, skip count, count by 10's
We can count to 100.
10, 20, 30, 40, (up to 100)
Shelby Star is my name
Shining brightly is my game
With five sparkly points and lots of sides, too
With wishes I make dreams come true.
I am Cindi Circle
Watch me turn
Round and round
And you will learn
I'm not straight and
I don't bend
My outside edges
Never end!
Sammy Square is my name
My four sides are just the same
Turn me around, I don't care
I'm always the same, I'm a square!
I am Danny Diamond
I am like a kite
But I'm really just a square
Whose corners are pulled tight
Ricky rectangle is my name
My four sides are not the same
Two are short and two are long
Count my sides, come along
1-2-3-4
Tommy Triangle is the name for me
Count my sides - there's 1-2-3
I am Ollie Oval
A football shape is mine
Some people think that I"m an egg
But I think I look fine!
OR
Opal Oval is my name.
The circle and I are not the same.
The circle is round, as round can be.
I am shaped like an egg as you can see
Harry Heart is my name
The shape I make is my fame
With a point on the bottom and two humps on top
When it comes to love I just can't stop!
1 A straight line down and 1 is done.
2 Around and back on the railroad track, 2,2,2.
(Read as "choo-choo-choo")
3 Go around and around a tree. That's the way to write a 3.
4 Down and across and down once more. That's way to write 4.
5 Down and around, make it fat. Numeral 5 wears a hat.
6 Down and around, make a loop. Numeral 6 rolls a hoop.
7 Across, slant, then you are done. Writing 7 can be fun.
8 Write an S but do not wait. Come back up and write an 8.
9 A loop and a line make numeral 9.
10 Pull down straight, lift, and then curve down, curve up--that's a 10.
Number Poem
Down you run and 1 is done.
Around, and down, and out go you,
That's the way to make a 2.
Around, and around, like a bee,
That's the way to make a 3.
Down, across, and down once more,
That's the way to make a 4.
Short neck, belly fat,
Number 5 wears a hat.
Down, around, in a circle you go,
That's a six, just as you know.
Straight across, slide down from heaven,
That's the way to make a 7.
First a snake, then come back straight,
That's the way to make an 8.
First a ball and then a line,
That's the way to make a 9.
Tall straight, circle then,
That's the way to make a 10
Circumference and Area
Fiddle de dum, Fiddle de dee,
A ring round the moon is pi times d;
But if a hole you want repaired,
You use the formula Pi r squared.
A New Solution to an Old Problem
By: Eleanor Ninestein
The Topologist's child was quite hyper
'Til she wore a Moebius diaper.
The mess on the inside
Was thus on the outside
And it was easy for someone to wipe her.
The Mobius Strip
A mathematician confided
That a Mobius band is one-sided.
And you'll get quite a laugh
If you cut it in half,
For it stays in one piece when divided.
Einstein
By: Katherine O'Brien
The Mathematics Teacher
April 1968
His first day at Princeton, the legend goes,
he went for a stroll (in his rumpled clothes).
He entered a coffee shop -- moment of doubt --
then climbed on a stool and looked about.
Beside him, a frosh, likewise strange and alone,
consoling himself with an ice cream cone.
Now Einstein's glee
was plain to see
at the sight of the cone with the sphere on top
(in the hand of a frosh in a sandwich shop)
and -- oh incredible --
completely edible!
He smiled at the frosh, then the waiter came,
and Einstein gestured he'd like the same, and they sat there nibbling, suddenly kin,
with no common language to verbalize in.
But foreign no longer, no longer alone,
with the fellowship bond of an ice cream cone.
Valentine
You disintegrate my differential,
You dislocate my focus.
My pulse goes up like an exponential
whenever you cross my locus.
Without you, sets are null and void --
so won't you be my cardioid?
Threes
By: John Atherton
I think that I shall never c
A # lovelier than 3;
For 3 < 6 or 4,
And than 1 it's slightly more.
All things in nature come in 3s,
Like ... , trio's, Q.E.D.s;
While $s gain more dignity
if augmented 3 x 3 --
A 3 whose slender curves are pressed
By banks, for compound interest;
Oh, would that, paying loans or rent,
My rates were only 3%!
3² expands with rapture free,
And reaches toward infinity;
3 complements each x and y,
And intimately lives with pi.
A circle's # of °
Are best ÷ up by 3s,
But wrapped in dim obscurity
Is the square root of 3.
Atoms are split by men like me,
But only God is 1 in 3.
learning insight res
Structure of CV/résumé
1. Personal details:
* name
* address (home and college address if different)
* telephone number (home/mobile/college if applicable)
* email address
* personal profile (a summary outlining who you are and why you're a worthwhile employment prospect for this particular job: you could also mention here that you're currently studying in higher education)
2. Employment history:
* begin with your most recent job, briefly outlining your role and responsibilities (especially those most relevant to the job you're applying for)
* working backwards, list any other jobs you've had in chronological order: don't go into great detail about these unless you want to highlight any aspects relevant to your application
* if you've had several less important jobs that aren't relevant to the job you're applying for, you can summarize these as, for example, 'various administrative posts'
* if you've been raising a family, unemployed, or taking another career break, say so: it can create a negative impression if you just leave gaps in your employment history
* treat any significant periods of unemployment in a positive way: you could outline any activities or initiatives you did, such as carrying out voluntary work
3. Education and qualifications:
* if you're still studying for a qualification in higher education, start with this: you could add a heading or subheading (for example, Current studies) to make it clear that your studies are ongoing
* if you've completed any other further or higher education, outline this next
* give your secondary school or schools and the dates you attended them, together with:
o a list of all your A-level (or Scottish Higher) subjects and grades
o brief details of GCSEs, Scottish Standard Grades, or equivalent qualifications (only give full details of these if the employer has specifically asked for them or the subjects are relevant to the job in question)
4. Any other skills, achievements, or training:
* list any relevant professional qualifications, courses, or training (e.g. IT qualifications, knowledge of a foreign language)
* mention significant awards, other achievements, relevant positions of responsibility, etc.
5. Interests or pastimes:
* a brief overview of your interests or hobbies will help your potential employer to gain an insight into the type of person you are
6. Referees:
* you can either give contact details of two people who'd be willing to give you a reference or say that references are available on request
* if you're providing specific names, you could choose one recent/relevant former employer and one current tutor
1. Personal details:
* name
* address (home and college address if different)
* telephone number (home/mobile/college if applicable)
* email address
* personal profile (a summary outlining who you are and why you're a worthwhile employment prospect for this particular job: you could also mention here that you're currently studying in higher education)
2. Employment history:
* begin with your most recent job, briefly outlining your role and responsibilities (especially those most relevant to the job you're applying for)
* working backwards, list any other jobs you've had in chronological order: don't go into great detail about these unless you want to highlight any aspects relevant to your application
* if you've had several less important jobs that aren't relevant to the job you're applying for, you can summarize these as, for example, 'various administrative posts'
* if you've been raising a family, unemployed, or taking another career break, say so: it can create a negative impression if you just leave gaps in your employment history
* treat any significant periods of unemployment in a positive way: you could outline any activities or initiatives you did, such as carrying out voluntary work
3. Education and qualifications:
* if you're still studying for a qualification in higher education, start with this: you could add a heading or subheading (for example, Current studies) to make it clear that your studies are ongoing
* if you've completed any other further or higher education, outline this next
* give your secondary school or schools and the dates you attended them, together with:
o a list of all your A-level (or Scottish Higher) subjects and grades
o brief details of GCSEs, Scottish Standard Grades, or equivalent qualifications (only give full details of these if the employer has specifically asked for them or the subjects are relevant to the job in question)
4. Any other skills, achievements, or training:
* list any relevant professional qualifications, courses, or training (e.g. IT qualifications, knowledge of a foreign language)
* mention significant awards, other achievements, relevant positions of responsibility, etc.
5. Interests or pastimes:
* a brief overview of your interests or hobbies will help your potential employer to gain an insight into the type of person you are
6. Referees:
* you can either give contact details of two people who'd be willing to give you a reference or say that references are available on request
* if you're providing specific names, you could choose one recent/relevant former employer and one current tutor
learnig insight app
Employers often receive hundreds of applications for every job, so it's vital to make sure that your CV/résumé and job application letter create the right impression and present your personal information in the most effective way.
Click here for more on job application letters and emails.
You'll also find extra information on writing CVs/résumé and job applications in the dictionary centre section.
Firstly, here are some general CV do's and don'ts:
DO
* read the advert carefully and tailor your CV/résumé to match the job you're applying for
* be concise when outlining your education and employment history
* try to keep your CV/résumé to one or two sides of A4 paper
* use brief, informative sentences, short paragraphs, and standard English
* structure your CV/résumé in a logical way, with a limited number of main sections
* begin with an action verb when describing your duties (see the CVs/résumé below)
* use bold type or bullet points to highlight key points
* proofread your work for spelling, grammar, and punctuation (many employers just discard job applications that contain such errors)
* see your college careers adviser: they'll have a range of sample CVs/résumés and will be able to help you when writing specific applications
* update your CV/résumé regularly, as your situation changes
DON'T
* go into too much detail: employers are too busy to read rambling and unfocused CVs/résumés
* leave gaps in your employment history: it's better to add a sentence explaining any periods that are unaccounted for (such as a gap year)
* forget to read your CV/résumé for both content and mistakes (you could also ask someone to read it for you)
* use many different typefaces: keep to one or two that are clear and easy to read
* brighten up your CV/résumé with inappropriate colour, photos, or graphics
* name people as referees unless you've already confirmed that they're happy to provide a reference for you
Here are some guidelines on two broad approaches to writing CVs/résumés, one suitable for students embarking on their careers who haven't had a full-time permanent job, and one for students who've worked for several years and who'll be returning to full-time work after their studies.
Starting out on a career
If you come to university or college directly from school, sixth-form college, or after a gap year, you're likely to be applying for your first full-time permanent job when your course ends. This means that, after giving your personal details, you should structure your CV/résumé in the way shown below, first outlining your education and qualifications and then any work experience, part-time or temporary jobs, and other skills.
Structure of CV/résumé
1. Personal details:
* name
* address (home and college address if different)
* telephone number (home/mobile/college if applicable)
* email address
* personal profile (a summary outlining who you are and why you're a worthwhile employment prospect for this particular job)
2. Education and qualifications:
* if you're studying for a qualification in higher education, start with this, making it clear that your studies are ongoing and when the course is due to end
* if you've completed any other further or higher education, state this next
* give your school or schools and the dates you attended them, together with:
o a list of all your A-level (or Scottish Higher) subjects and grades
o brief details of GCSEs, Scottish Standard Grades, or equivalent qualifications (only give full details of these if the employer has specifically asked for them or the subjects are relevant to the job in question)
3. Employment history:
* if you've had several temporary or part-time jobs, list the most important in chronological order, starting with the most recent
* give a brief summary of your roles and responsibilities, focusing on those most relevant to the post you're applying for
* if you've worked in a variety of short-term jobs that aren't relevant to your current application, you can summarize these as, for example, 'various temporary retail posts'
4. Any other skills, achievements, or training:
* list any relevant courses or training (e.g. IT qualifications, knowledge of a foreign language)
* mention significant awards and other achievements, or positions of responsibility at college
5. Interests or pastimes:
* a brief overview of your interests or hobbies will help your potential employer to gain an insight into the type of person you are
6. Referees:
* you can either give contact details of two people who'd be willing to give you a reference or say that references are available on request
* if you're providing specific names and this is your first job, you could use a tutor, teacher, or anyone (apart from your family) who knows you well enough to vouch for you
Click here for more on job application letters and emails.
You'll also find extra information on writing CVs/résumé and job applications in the dictionary centre section.
Firstly, here are some general CV do's and don'ts:
DO
* read the advert carefully and tailor your CV/résumé to match the job you're applying for
* be concise when outlining your education and employment history
* try to keep your CV/résumé to one or two sides of A4 paper
* use brief, informative sentences, short paragraphs, and standard English
* structure your CV/résumé in a logical way, with a limited number of main sections
* begin with an action verb when describing your duties (see the CVs/résumé below)
* use bold type or bullet points to highlight key points
* proofread your work for spelling, grammar, and punctuation (many employers just discard job applications that contain such errors)
* see your college careers adviser: they'll have a range of sample CVs/résumés and will be able to help you when writing specific applications
* update your CV/résumé regularly, as your situation changes
DON'T
* go into too much detail: employers are too busy to read rambling and unfocused CVs/résumés
* leave gaps in your employment history: it's better to add a sentence explaining any periods that are unaccounted for (such as a gap year)
* forget to read your CV/résumé for both content and mistakes (you could also ask someone to read it for you)
* use many different typefaces: keep to one or two that are clear and easy to read
* brighten up your CV/résumé with inappropriate colour, photos, or graphics
* name people as referees unless you've already confirmed that they're happy to provide a reference for you
Here are some guidelines on two broad approaches to writing CVs/résumés, one suitable for students embarking on their careers who haven't had a full-time permanent job, and one for students who've worked for several years and who'll be returning to full-time work after their studies.
Starting out on a career
If you come to university or college directly from school, sixth-form college, or after a gap year, you're likely to be applying for your first full-time permanent job when your course ends. This means that, after giving your personal details, you should structure your CV/résumé in the way shown below, first outlining your education and qualifications and then any work experience, part-time or temporary jobs, and other skills.
Structure of CV/résumé
1. Personal details:
* name
* address (home and college address if different)
* telephone number (home/mobile/college if applicable)
* email address
* personal profile (a summary outlining who you are and why you're a worthwhile employment prospect for this particular job)
2. Education and qualifications:
* if you're studying for a qualification in higher education, start with this, making it clear that your studies are ongoing and when the course is due to end
* if you've completed any other further or higher education, state this next
* give your school or schools and the dates you attended them, together with:
o a list of all your A-level (or Scottish Higher) subjects and grades
o brief details of GCSEs, Scottish Standard Grades, or equivalent qualifications (only give full details of these if the employer has specifically asked for them or the subjects are relevant to the job in question)
3. Employment history:
* if you've had several temporary or part-time jobs, list the most important in chronological order, starting with the most recent
* give a brief summary of your roles and responsibilities, focusing on those most relevant to the post you're applying for
* if you've worked in a variety of short-term jobs that aren't relevant to your current application, you can summarize these as, for example, 'various temporary retail posts'
4. Any other skills, achievements, or training:
* list any relevant courses or training (e.g. IT qualifications, knowledge of a foreign language)
* mention significant awards and other achievements, or positions of responsibility at college
5. Interests or pastimes:
* a brief overview of your interests or hobbies will help your potential employer to gain an insight into the type of person you are
6. Referees:
* you can either give contact details of two people who'd be willing to give you a reference or say that references are available on request
* if you're providing specific names and this is your first job, you could use a tutor, teacher, or anyone (apart from your family) who knows you well enough to vouch for you
What Is Insight Learning?
By an eHow Contributor
I want to do this! What's This?
Insight learning involves a sudden realization distinct from cause-and-effect problem solving. Insight learning manifests as a spontaneous occurrence, and is a noteworthy phenomenon in the learning process. Insight learning can also be described as "an epiphany" and "eureka."
The Anatomy of Insight Learning
1. The experience of insight learning often involves three factors:
1. Seemingly all possible problem-solving attempts have been exhausted and are unsuccessful.
2. Ongoing attempts to solve an apparently unsolvable problem eventually end.
3. A perfect solution to the problem is suddenly realized in a spontaneous way.
Wolfgang Köhler
2. According to the Encyclopedia Britannica, Wolfgang Köhler was a psychologist who conducted experiments in which insight learning was observed in animal behavior. Wolfgang Köhler's research significantly contributed to the understanding of insight learning.
Animal Behavior Studies
3. According to Wolfgang Köhler's experiments, insight learning is observable when studying problem-solving behavior in chimpanzees. In one experiment, after a chimpanzee was given two short sticks with a banana set out of reach, insight learning eventually occurred. After unsuccessfully attempting to reach the banana with the short sticks, the hungry chimpanzee gave up. However, the chimpanzee later accidentally discovered that the sticks could be joined together to form one longer stick. Just then, a spark of insight revealing a solution manifested, allowing the chimpanzee to successfully reach the banana.
Epiphany
4. Another noteworthy term that describes insight learning is "epiphany." Epiphanies involve a sudden revelation or abrupt awareness bringing seemingly chaotic data into symmetry. Experiencing an epiphany is often associated with the feeling of having a sudden leap of understanding. The opposite of insight learning would be insight achieved through a gradual building up of knowledge leading to a successful solution.
Eureka
5. Insight learning also involves the "I have found it!" feeling or "eureka," a Greek word representing this affirmation. Insight learning is also expressed as the "Aha moment," accompanying the sensation of suddenly knowing something after the disenchantment of being uninformed
I want to do this! What's This?
Insight learning involves a sudden realization distinct from cause-and-effect problem solving. Insight learning manifests as a spontaneous occurrence, and is a noteworthy phenomenon in the learning process. Insight learning can also be described as "an epiphany" and "eureka."
The Anatomy of Insight Learning
1. The experience of insight learning often involves three factors:
1. Seemingly all possible problem-solving attempts have been exhausted and are unsuccessful.
2. Ongoing attempts to solve an apparently unsolvable problem eventually end.
3. A perfect solution to the problem is suddenly realized in a spontaneous way.
Wolfgang Köhler
2. According to the Encyclopedia Britannica, Wolfgang Köhler was a psychologist who conducted experiments in which insight learning was observed in animal behavior. Wolfgang Köhler's research significantly contributed to the understanding of insight learning.
Animal Behavior Studies
3. According to Wolfgang Köhler's experiments, insight learning is observable when studying problem-solving behavior in chimpanzees. In one experiment, after a chimpanzee was given two short sticks with a banana set out of reach, insight learning eventually occurred. After unsuccessfully attempting to reach the banana with the short sticks, the hungry chimpanzee gave up. However, the chimpanzee later accidentally discovered that the sticks could be joined together to form one longer stick. Just then, a spark of insight revealing a solution manifested, allowing the chimpanzee to successfully reach the banana.
Epiphany
4. Another noteworthy term that describes insight learning is "epiphany." Epiphanies involve a sudden revelation or abrupt awareness bringing seemingly chaotic data into symmetry. Experiencing an epiphany is often associated with the feeling of having a sudden leap of understanding. The opposite of insight learning would be insight achieved through a gradual building up of knowledge leading to a successful solution.
Eureka
5. Insight learning also involves the "I have found it!" feeling or "eureka," a Greek word representing this affirmation. Insight learning is also expressed as the "Aha moment," accompanying the sensation of suddenly knowing something after the disenchantment of being uninformed
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