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Questions and Answers
How can the length of a closed piecewise smooth plane curve be computed?
How can the length of a closed piecewise smooth plane curve be computed?
- $L = x'(a) - x'(b) + y'(a) - y'(b)$
- $L = x(b) - x(a) + y(b) - y(a)$
- $L = \int_{a}^{b}{\sqrt{x'(t)^{2}+y'(t)^{2}}}\,\mathrm{d}t$ (correct)
- $L = \int_{a}^{b}{x'(t) + y'(t)}\,\mathrm{d}t$
Who is known to have approximated the perimeter of a circle by surrounding it with regular polygons?
Who is known to have approximated the perimeter of a circle by surrounding it with regular polygons?
- Euclid
- Archimedes (correct)
- Newton
- Pythagoras
What theory describes a generalized notion of perimeter for hypersurfaces bounding volumes in n-dimensional Euclidean spaces?
What theory describes a generalized notion of perimeter for hypersurfaces bounding volumes in n-dimensional Euclidean spaces?
- Euler's Theorem
- Caccioppoli sets (correct)
- Fourier Analysis
- Cantor's Set Theory
Why are polygons fundamental to determining perimeters?
Why are polygons fundamental to determining perimeters?
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What is the formula for calculating the perimeter of a polygon?
What is the formula for calculating the perimeter of a polygon?
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