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Curiosity about infinity in geometry(Not homework just curious) 
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#1
Feb2214, 11:34 PM

P: 42

Okay, let's say you have an infinitely long line segment.
Using area and volume formulas for different shapes, would you get an infinitely large shape that the formula was for in the first place? Area: For rectangles, would you get an infinitely large rectangle with A = l * w? What about triangles with 1/2 * b * h? What about squares with l^2 what about rombi with A = b * h? what about trapezoids with A = ((b1 + b2)*h)/2? what about pentagons with A = 5/2 * l * a(apothem)? hexagons with A = (3√3 s2)/ 2? what about other regular polygons with Area = (a(apothem) x p(perimeter))/2? what about ellipses with π * vertical radius * horizontal radius? What about circles with π * r^2 Volume: What about spheres with V = ⁴⁄₃πr³? What about triangular prisms with 1/2 x b x h x l? what about other prisms with V = area of base * l (yes that includes the cylinder at the infinite end)? what about dodecahedrons with (15+7×√5)/4 × (Edge Length)^3 what about octahedrons with (√2)/3 × (Edge Length)^3 what about Icosahedrons with 5×(3+√5)/12 × (Edge Length)^3 What about toruses that have holes with 2 × π^2 × R(radius of hole) × r^2(radius of circular cross section)? What about cones with π × r^2 × (h/3)? 


#2
Feb2314, 02:47 AM

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What do you think?



#3
Feb2314, 03:01 PM

P: 42

I think that you would get an infinitely large shape from an infinitely long line segment but I honestly don't know.



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