You did not answer the two questions I gave you.

]]>I thought you used your old configuration. Now I find you used my suggestion and took A(0,0) B(a,b) and C(c,0) the slopes you got are correct.But AB=AC . this gives which gives Now the product of slopes is -1.]]>

Textbooks all have one mother. Two million years ago some hairy ape-man or man-ape depending on which anthropologist you talk to, wrote the first one. It was written on clay tablets and weighed about 2500 tons. Since then all authors have read that book and created their own condensed version of it. Essentially, they read a very big ( and heavy ) book and wrote a smaller and lighter one. Since that mother of all math textbooks was an utter bore the children can be not be much different.

I like Martin Gardner books.

]]>I'm after a short, simple but correct explanation for children ~10 years old of why the Euler Characteristic is a 'basic idea in topology' (as I've read). It's for use as a 'by the way, you might be interested to know...' insight into more advanced maths to conclude an exercise of counting faces, vertices and edges of common 3D shapes, and discovering that they usually have an Euler Characteristic of 2 (The only exception I've been able to think of among common 3D shapes is a cylinder, which I think has 3 faces, 0 vertices and 2 edges, so an Euler Characteristic of 1.).

Thanks for your help!

]]>Can anybody explain to me clearly on this formula, in particular on how to use it. Please show step-by-step if possible.

Thanks!]]>

That works on a problem I used it on. Very good!

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