The Deltoid is a Kakeya Set
The Deltoid is a Kakeya Set
A circle of radius 1 rolls inside a fixed circle of radius 3 (the fixed circle is shown when "labels" is selected); a point on the circumference of traces out the green curve, called a deltoid (or tricuspoid). Let the tangent to the deltoid at meet the deltoid again at and . Then the midpoint of lies on the circle of radius 1 with center at origin. The length of is 4, so the deltoid is a Kakeya set: a set through which a line segment can be moved back to itself but turned 180°.
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