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Math · Advanced

Famous Curves

Which slide gets a ball to the bottom fastest? What shape does a hanging chain make? Why do soap bubbles meet at 120°? Meet the cycloid, the catenary, minimal surfaces and shapes of constant width, and find out why the circle encloses the most area: curves that nature and mathematicians found by asking what is "best".

7 lessons~35 min0/7 complete
1

The Fastest Path

Brachistochrone and cycloid.

  1. The BrachistochroneShortest isn’t fastest
  2. The Rolling WheelThe cycloid and the tautochrone
2

Nature’s Optimisers

Chains and soap films.

  1. The Hanging ChainCatenary, not parabola
  2. Soap FilmsMinimal surfaces and 120°
3

Shapes with a Superpower

Constant width, and the most area for a given fence.

  1. Constant WidthRollers that aren’t round
  2. Most Area, Least FenceWhy the circle is special
  3. The Logarithmic SpiralGrowth without changing shape