[megachirops]

I' am learning the Pythagorean Therom in my Geometry class right now and i am totaly lost!! Help Please!!

[DrRocket]

megachirops, on 30 January 2012 - 12:20 AM, said:

I' am learning the Pythagorean Therom in my Geometry class right now and i am totaly lost!! Help Please!!

What is your question ?

[Keenidiot]

The Theorum states that the hypotenuse of a triangle with a right angle is equal to the measure of each side squared and added together:

a²+b²=C²



So, for example, if you have a right triangle with two sides that measure 4 and 5, then you'd plug them into the formula above.

a²⁺b²=c²

4² + 5²=c²


Which would simplify out to:
16 + 25 = C²


41=c²


You'd then take the square of 41, and that would be the measure of the hypotenuse.


So, what's your question?

[TonyMcC]

I think it's worth noting that the geometrical proof has nothing to do with numbers per se. Its about areas. There are several proofs in the link. The one I used in school was proof 12 for example. http://www.cut-the-k...org/pythagoras/

This post has been edited by TonyMcC: 30 January 2012 - 11:27 AM

[megachirops]

Keenidiot, on 30 January 2012 - 05:59 AM, said:

The Theorum states that the hypotenuse of a triangle with a right angle is equal to the measure of each side squared and added together:

a²+b²=C²



So, for example, if you have a right triangle with two sides that measure 4 and 5, then you'd plug them into the formula above.

a²⁺b²=c²
4² + 5²=c²


Which would simplify out to:
16 + 25 = C²

41=c²


You'd then take the square of 41, and that would be the measure of the hypotenuse.

So, what's your question?

Thanks that answers my question, i was confused on the steps of the problem, my teacher just rushed through this therom and i was left stranded! Thanks!

[DrRocket]

TonyMcC, on 30 January 2012 - 11:27 AM, said:

I think it's worth noting that the geometrical proof has nothing to do with numbers per se. Its about areas. There are several proofs in the link. The one I used in school was proof 12 for example. http://www.cut-the-k...org/pythagoras/

The Pythagorean theorem is only periphally about area.

What distinguishes Euclidean geometry from non-Euclidean (planar) geometries is the parallel postulate: Given a line and a point not on the line there is a unique line through that point parallel to the given line.

It is not obvious, but the Pythagorean theorem is equivalent to the parallel postulate. It is quite proper to say that the Pythagorean theorem characterizes Eucllidean geometry in the plane. One can extend that to the fact that it is the Pythagorean theorem that gives us the usual notion of distance and it is that notion of distance that characterizes Euclidean geometries in higher dimensions -- and that is what distinguishes the Euclidean model that we learn in high school from the model that seems to actually describe the universe as one lerns in general relativity.

So, no matter what specific proof and bag of tricks you use to prove the Pythagorean theorem, you can be sure that in any valid proof the parallel postulate will play a role somewhere, either directly or in the proof of a result that is in turn used to prove the theorem.

[TonyMcC]

DrRocket, on 5 February 2012 - 12:56 AM, said:

The Pythagorean theorem is only periphally about area.

What distinguishes Euclidean geometry from non-Euclidean (planar) geometries is the parallel postulate: Given a line and a point not on the line there is a unique line through that point parallel to the given line.

It is not obvious, but the Pythagorean theorem is equivalent to the parallel postulate. It is quite proper to say that the Pythagorean theorem characterizes Eucllidean geometry in the plane. One can extend that to the fact that it is the Pythagorean theorem that gives us the usual notion of distance and it is that notion of distance that characterizes Euclidean geometries in higher dimensions -- and that is what distinguishes the Euclidean model that we learn in high school from the model that seems to actually describe the universe as one lerns in general relativity.

So, no matter what specific proof and bag of tricks you use to prove the Pythagorean theorem, you can be sure that in any valid proof the parallel postulate will play a role somewhere, either directly or in the proof of a result that is in turn used to prove the theorem.

I left school at 16 so my maths is pretty basic. I believe that the parallel postulate is only applicable to Euclidean geometry (i.e. applicable to a plane).
It seems to me that if you draw a right angled triangle and place three dots at different distances from each of the sides and draw lines parallel to the sides you will draw another right angled triangle. The basic proof of the addition of areas will apply to the triangle you have just drawn. I'm probably missing something, if so I apologise.