They are all pretty fukcing obvious
2006-09-01 16:21:58 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
One never knows when a measure of rope will be needed to fashion a hypoteneuse to hang from .. Euclid was a freaking pedant!
2006-09-01 16:54:51 · answer #1 · answered by gmonkai 4 · 0⤊ 0⤋
Euclidean Geometry is a system of proofs of theorems based on the axioms and postulates. You're right in part -- many of them appear obvious and straightforward, but not all the proofs of the theorems are so obvious, yet they all follow from the axioms and postulates.
2006-09-01 23:26:41 · answer #2 · answered by birchardvilleobservatory 7 · 0⤊ 0⤋
Because, it's Geometry, it didn't just appear one day. The study of Geometry slowly evolved like any other science/study. So that means it had to start from nothing, to something. So grasping the concepts of formal shapes and so on was born.
Look at it this way, 1+1=2. It's obvious and simple right? But it couldn't be skipped in its creation, because than we wouldn't have the complexe equation sheets, etc. that we have now.
2006-09-01 23:36:36 · answer #3 · answered by Justin t 1 · 0⤊ 0⤋
Any branch of mathematics begins with a set of statements accepted as the basis of the dicussion. From these basic statements, valid conclusions are drawn by the use of logic to build a more complex mathematical system.
In other words, you start with the obvious, then prove the not so obvious from deduction.
2006-09-02 00:03:16 · answer #4 · answered by Jerry M 3 · 1⤊ 0⤋
Obvious they may appear to be, but the point of studying them is to be familiar with the use of logic, applied in a stepwise fashion. And, some of them are not as obvious as may first appear: consider "It is possible to draw exactly one line, parallel to a given line, through a point not on the line." This is true for plane geometry, but for spherical geometry it turns out to be "It is possible to draw no line, parallel to a given line, through a point not on the line." Lots of higher mathematics has been built using this stuff.
2006-09-02 00:23:43 · answer #5 · answered by Anonymous · 0⤊ 0⤋
they form the framework for helping the human mind learn to reason with precision if need be.
without them a lot of sloppy thought would be an alternative
would you want to fly in an airplane designed by someone who was not familiar with Euclidean concepts?
2006-09-02 00:03:08 · answer #6 · answered by atheistforthebirthofjesus 6 · 0⤊ 0⤋