In other words, did we discover the Pythagorean theorem or did we invent it? All the right triangles I can find certainly obey square a + square b = the square of the hypotenuse law so in that regard it seems like we discovered some law of nature. On the other hand, the whole concept of mathematics seems contrived in that we set down certain assumptions about equations that donвЂ™t really exist in the real world. Sometimes I think that the whole system of mathematics is a result of how our brain evolved (or was created if that is your thing). I don t know why it would be productive to worry about such a thing, but I do.

its all man-made. The idea of an infinite line going straight in each direction is crazy when one thinks of how space is curved.

Therefor any line-segment, including the ones in a triangle, cannot be calculated to an exact digit.

Our man-made math does to a pretty good job, when we use such small line-segments, to help determine required lengths of ladders to get on your roof.

REMEMBER: math is a drive to understand and cope with a diverse world. Nothing is completely identical to anything else, but to set up scenarios close to nature is helpful to control it.

If you want to think about something, why not try the same thing I am.

Check out the link below, maybe you can help me with my problem.

I have tried A&O history and found it to be flawed. We have just started Saxon and I am very impressed. There is a new system out called Teaching Textbooks which provides more detailed instruction in the text and also with a CD. I think it is probably good especially for the mathaphobe. Saxon is great, and you can sell the book afterwards.

They are discoveries. Theory of simple Lever is a discovery. If we use it for lifting a weight, then it is an invention.

In general, humanity discover Scientific laws and invent engineering methods for commercial utilisation of discovered scientific laws. Incidently this is a definition of Engineering.