- #1
MarekS
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After reading the article on Poincare's conjecture in the Economist, I became curious about simplified 3-dimensional objects.
Excerpt:
Let's take a cube and simplify it into a circle. Could we then use equations ment for circles for the simplified shape, ie calculate the cube's surface area using S=pii*radius²?
How would the math look like for such calculations?
MarekS
Excerpt:
To understand the Poincaré conjecture, start by thinking of any object existing in a three-dimensional world. Although it is usual to think of the object as three-dimensional, mathematicians consider only the surface of these objects—which are two-dimensional. All objects in a three-dimensional world can be simplified by smoothing out their shape to look like either a two-dimensional sphere (otherwise known as a circle) or a two-dimensional torus with however many holes necessary. To mathematicians, a chair is equivalent to an apple; a mug—at least, one with a handle—is like a doughnut.
Let's take a cube and simplify it into a circle. Could we then use equations ment for circles for the simplified shape, ie calculate the cube's surface area using S=pii*radius²?
How would the math look like for such calculations?
MarekS