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"The purpose of geometry is to make clear to students the meaning of demonstration, the meaning of mathematical precision and the pleasure of discovering absolute truth. If demonstrative geometry is not taught to enable a pupil to have the satisfaction of proving something, ..., then it is not worth teaching at all." W.D. Reeve (1930)
"Geometry achieves it highest possibilities if, in addition to direct and practical usefulness, it can establish a pattern of reasoning; if it can develop the power to think clearly in geometric situations, and to use the same discrimination in non-geometric situations." H. C. Christofferson (1930)
"I firmly believe that the reason we teach demonstrative geometry in our high schools today is to give pupils certain ideas about the nature of proof. The great majority of teachers of geometry hold this same point of view. 2 Our great aim in the tenth year is to teach the nature of deductive proof and to furnish pupils with a model of all their life thinking." C. B. Upton, (1930)
The Teachers will endeavor to combine mildness with firmness, kindness with justice. Strict regard will also be had to the language, the manners, the whole deportment of the pupils, in the school room and out of it, so as to secure, if possible, not only that they may become good scholars, but also good men and women. Students who will not refrain from drunkenness and other vicious indulgences, will be promptly dismissed, as dangerous to the morals of the school, and unworthy of a place in it or any other.
The followers of the Greek pilosopher Epicurus, who esteemed feeling over reasoning, had no patience for the arguments of Euclid. His science is ridiculous, they said, pointing to a proposition half way through the first book of the Elements, in which Euclid labours to show that no side of a triangle can be longer than the sum of the other two sides.
'It is evident even to an jackass.' For a hungry jackass, standing at A (Fig. 1.1.2) will go directly to a bale of hay at B. without passing through any point C outside the straight line AB. The beast's geometrical intuition tells him that AB must be shorter than AC + CB.
The charge that Euclid stops to prove propositions evident even to an ass has ecoed thorugh the ages.
One of the echoers was the seventeenth-century philosopher and mathematician Blaise Pascal, who accused his fellow geometers of six perennial faults, among them 'proving things that have no need of proof'. He took as his example Euclid's compusion to demonstrate that two sides of a triangle taken together exceed the third. To this objection the Greek philosophical geometer Proclus, who wrote a lengthy commentary on the Elements early in the fifth century, had replied that a proposition evident to the senses 'is still not clear for scientific thought'.
-Geometry Civilized
Originally posted by ABNARTY
I am not really sure where you are going with the whole thing. Maybe it is pure comparative analysis and I am looking for a solution where none was presented.
The purpose of geometry is to make clear to students the meaning of demonstration, the meaning of mathematical precision and the pleasure of discovering absolute truth.
Originally posted by Northwarden
Today's society largely breeds specialists instead
Originally posted by delicatessen
are you talking about deductive reasoning (base for geometry) or education? or is this thread about morals?
Originally posted by davespanners
It's amazing that with such great schooling in critical thinking and reading Latin that in the 1890's over 13% of the population were illiterate, and now with the terrible modern education system the rate is way below 1%
Originally posted by davidgrouchy
That is to say that geometry was not taught just so people could bisect a figure, or calculate the length of one side of a triangle, but geometry was taught as the foundation of critical thinking. That quite literally thought is best understood and analyzed when it has a definet shape. This may sound quite alien in this day and age. But consider the legal profession as shown on TV.
Even in the media we still hear the phrases "to the point," "line of reasoning," and "Don't be obtuse." all of which come from geometry.
If our young men miscarry in their first enterprises, they lose all heart. If the young merchant fails, men say he is _ruined_. If the finest genius studies at one of our colleges, and is not installed in an office within one year afterwards in the cities or suburbs of Boston or New York, it seems to his friends and to himself that he is right in being disheartened, and in complaining the rest of his life. A sturdy lad from New Hampshire or Vermont, who in turn tries all the professions, who teams it, farms it, peddles, keeps a school, preaches, edits a newspaper, goes to Congress, buys a township, and so forth, in successive years, and always, like a cat, falls on his feet, is worth a hundred of these city dolls. He walks abreast with his days, and feels no shame in not `studying a profession,' for he does not postpone his life, but lives already. He has not one chance, but a hundred chances. Let a Stoic open the resources of man, and tell men they are not leaning willows, but can and must detach themselves; that with the exercise of self-trust, new powers shall appear; that a man is the word made flesh, born to shed healing to the nations, that he should be ashamed of our compassion, and that the moment he acts from himself, tossing the laws, the books, idolatries, and customs out of the window, we pity him no more, but thank and revere him, -- and that teacher shall restore the life of man to splendor, and make his name dear to all history.
Originally posted by delicatessen
i take it mr David is just training to be a writer. geometry is not removed from school curricula.
Euclidean geometry is still taught in schools for purpose of developing mathematical reasoning skills, but is not significant for science and engineering anymore. there`s much more powerful and precise tool called calculus.
besides the OP lacks some logical glue between paragraphs. have you taken geometry course before?
Common notion 1.
Things which equal the same thing also equal one another.
Common notion 2.
If equals are added to equals, then the wholes are equal.
Common notion 3.
If equals are subtracted from equals, then the remainders are equal.
Common notion 4.
Things which coincide with one another equal one another.
Common notion 5.
The whole is greater than the part.
Originally posted by davidgrouchy
Originally posted by delicatessen
are you talking about deductive reasoning (base for geometry) or education? or is this thread about morals?
I'm speaking to the subject of education in this way. What permission do we give ourselves, in learning. To we give ourselves permission to learn everything? Why not. If no one is putting this expectation on us from the outside, are we being fair with ourselves to say "I'm entitled to know everything." I hazard a yes.
Originally posted by delicatessen
Originally posted by davidgrouchy
That is to say that geometry was not taught just so people could bisect a figure, or calculate the length of one side of a triangle, but geometry was taught as the foundation of critical thinking. That quite literally thought is best understood and analyzed when it has a definet shape. This may sound quite alien in this day and age. But consider the legal profession as shown on TV.
Even in the media we still hear the phrases "to the point," "line of reasoning," and "Don't be obtuse." all of which come from geometry.
excuse me, but how does it "sound alien in this day and age"? last i checked Euclidean geometry or the purpose it`s taught didnt change. you cant just get by without deductive reasoning in calculus. besides calculus is much trickier than straightforward simple logic of Euclidean geometry. let alone calculus is much younger than classical geometry if this thread`s goal is just to be a cheap shot at today`s society and it`s alleged low standards.
Originally posted by delicatessen
man, are you smoking something? so much for the thread with the word geometry in the title. this rhetoric probably may impress others, but it would be helpful if you stayed logical. what does all of this have to do with geometry?
The purpose of geometry is to make clear to students the meaning of demonstration, the meaning of mathematical precision and the pleasure of discovering absolute truth.
Originally posted by davidgrouchy
I accept everything said as a valid criticism.
Yes, I could have, and should have glued the post together better.
Calculus is not only more powerful and precise, it is easier than other maths.
All this I learned in High School with my physics nerd friends, and I should have related some personal stories to this end.
Found guilty but still trying to plead my cause I can only say that; while geometry is still taught in school. It is not taught as the foundation of critical thinking. The kind used in a court of law. The kind used to define what is, and is not, evidence.
What I have so spectacularly failed to convey is that geometry, once apon a time, was a tool to teach critical thinking. The kind used in Law, buisness, contracts, government, and to make people immune to being manipulated by hearsay or excessive emotionality.
I think the Media has done a lot help make sure that geometry is seen as obsolete, and doing what feels good as ultimate justice.
In way of supporting evidence of what Geometry used to be I present the five common notions. Not for you Delicatessen, as I'm confident you have more than a passing knowledge of them, but for the benefit of anyone reading who may be thinking, "what the H are they talking about."
Common notion 1.
Things which equal the same thing also equal one another.
Common notion 2.
If equals are added to equals, then the wholes are equal.
Common notion 3.
If equals are subtracted from equals, then the remainders are equal.
Common notion 4.
Things which coincide with one another equal one another.
Common notion 5.
The whole is greater than the part.
Originally posted by delicatessen
10 years ago in a post Soviet high school that i graduated geometry was taught the traditional way.