of proofs; in Geometry I, mean. I hated those things; it's not that they were difficult; I was just unable to see what I would do with those things in the real world.
2007-10-24 04:09:58 · 13 answers · asked by Usagi's Twin; HAJI IS MINE! 4 in Science & Mathematics ➔ Mathematics
Teaches sequential, logical reasoning.
2007-10-24 04:28:26 · answer #1 · answered by davidosterberg1 6 · 1⤊ 0⤋
I've come to the conclusion that high school geometry really isn't about geometry. It's about proofs, and the geometric objects simply provide us something concrete to prove theorems about. Few people would say, "gosh, I really doubted the assertion that opposite vertical angles are equal until I proved it." The point of the proof is not the conclusion, but the process of getting there.
Liking or not liking the subject is a matter of taste, of course. But any subject in which the main focus is the beauty of the journey rather than the destination appeals to me. More 'goal oriented ' folks might feel differently.
It's like the old joke about the two perplexed space aliens watching humans play golf: "If the goal is to get the ball in the hole, why don't they just pick it up and drop it in?" With each proposition to be proven, all the previously proved theorems are the set of "clubs" you have available for playing that particular hole.
In fact, in higher mathematics, mathematicians often seek new proofs of theorems that have already been proven. The goal is to find arguments that are more elegant, more beautiful. To take the analogy with golf: how few golf clubs (theorems) can you get away with using? Can you get off a really nice shot that will land you close to the hole with one brilliantly arcing piece of logic? Or will you just "putter along" with a long uninspired proof that eventually gets you there, but is not very exciting?
Again, different people have different esthetic senses, different ideas about beauty. It's certainly valid to say "I don't find geometry beautiful." But we don't judge a poem or painting on the basis of how it's applicable in the real world. If we judged other fields of human creativity by that same standard of "usefulness" that so many want to use for judging geometry, then the highest form of poetry ever written would be advertising jingles.
Let's not trivialize poetry, and let's not trivialize the logical structure of geometry, by refusing to acknowledge that in each case the greatness of the subject lies in the creative process that generates it rather than the utility of the results.
2007-10-24 12:03:49 · answer #2 · answered by Michael M 7 · 0⤊ 0⤋
The branches in philosophizing is 1. knowing for the sake of producing which we call art, 2. knowing for the sake of practicing which we call ethics but there is the hardest of all 3. knowing for the sake of knowing which we call speculative. After all knowing whatever branch it may belong makes us enjoy the intellectual delights rather than cater to our base passion. You may use it or not but the most important thing is that it has also even at minimal a reason and therefore we cannot just dismiss Geometry as something which is useless and therefore an object of hatred.
2007-10-24 11:27:18 · answer #3 · answered by Jun Agruda 7 · 3⤊ 0⤋
The point of proofs is not their usefulness in the real world (although they are in some cases) but the beauty of proofs lies in their generality and the deeper level of understanding you get (different from the knowledge you get by doing computation). A simple and elementary example is to prove that the sum of two odd numbers is even. Try it. (If you are not successful, google it.) If you are successful, try proving that there are an infinite number of primes (this one is harder -- think about how such a proof might look like and then look it up using google).
2007-10-24 11:22:42 · answer #4 · answered by Vic 4 · 2⤊ 0⤋
Geometry or like any other applied Mathematics are just tools for understanding the concepts in solving physical problems.
Proofs of any of the theorems, are created and constructed for their relevance in a sound judgment or reasoning.which may enforced the explanations in any physical problem solving.
2007-10-24 11:19:00 · answer #5 · answered by rene c 4 · 2⤊ 0⤋
i was joking but without all that geometry and all that proof you would never know how long or how large is your yard neverless all other things you enjoy yourself like traveling in air ,car or walking from point a to point b. good luck with your geometry.
2007-10-24 11:18:31 · answer #6 · answered by laura 2 · 0⤊ 0⤋
To define a theoretical point we have two manners
1) When two perpendicular lines of 'infinitesimal line thickness' intersect on a plane said point of intersection is a 2D point.
2) When two mutually perpendicular lines of 'infinitesimal line thickness' just meet each other on a plane (either by not intersecting each other or without a gap in between them) said point of meeting is also regarded a 2D point!
Theoritically 3D points are extensions of above two explanations.
With regards!
2007-10-24 13:43:03 · answer #7 · answered by kkr 3 · 0⤊ 0⤋
Teaches simple problem solving...and most importantly logic.
It is useful in the real world to keep people from taking advantage of your ignorance.
2007-10-24 11:19:50 · answer #8 · answered by runningman022003 7 · 2⤊ 0⤋
It teaches your mind to take a given set of facts and use them to prove a new fact.
Or it is in the curriculum to purposely annoy you and can thus be ignored.
Take your pick.
2007-10-24 11:16:56 · answer #9 · answered by Anonymous · 2⤊ 0⤋
i feel really stupid now. i'm currently learning about geometry. I KNOW! i'll ask my teacher tomorrow!
2007-10-24 16:13:12 · answer #10 · answered by Pappenheimer 4 · 0⤊ 0⤋