2D Geometry

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Main Question or Discussion Point

Does anyone have any useful websites for 2D geometry that discuss some more advanced concepts for a person interested in more of the "backbone" of geometry?

For example, instead of what the usual high school geometry course covers, some more in-depth knowledge of geometry would be great!
 

Answers and Replies

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Concerning geometry I have tought of something. Per exemple to calculate the volume of a "perfect" pyramid, you would have to imagine an infinite number of square composing it. The area of a square decreases with the height of the triangle. It is easy to find a function of the area of the square depending on this lenght. Graphing this function would give you a curve, and intergrating the area from the area point (0,0) to (final lenghts, final area) would perhaps give you the right result. The reason I think it would be correct is that if you calculate the area, you would have to find a function of the perimeter instead of the area. Since this function is linear, I was able to find that it was correct...
 
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Werg22 said:
Concerning geometry I have tought of something. Per exemple to calculate the volume of a "perfect" pyramid, you would have to imagine an infinite number of square composing it. The area of a square decreases with the height of the triangle. It is easy to find a function of the area of the square depending on this lenght. Graphing this function would give you a curve, and intergrating the area from the area point (0,0) to (final lenghts, final area) would perhaps give you the right result. The reason I think it would be correct is that if you calculate the area, you would have to find a function of the perimeter instead of the area. Since this function is linear, I was able to find that it was correct...
I don't think that is the question though. I mean, you could find the volume of a perfect pyramid with something like the following:

[tex]\sum (h-y)\Delta y=\int_{0}^{h}(h-y)^{2}dy=\frac{h^{3}}{3}[/tex]

...but without calculus, how would it be done? Is that what you're asking?
 

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