## deltoidtricuspoid or Steiner's hypocycloid
after the Swiss mathematician Jakob Steiner
who investigated the curve in 1856. The deltoid, so-named because it looks like an uppercase Greek delta (Δ), is formed by a point on the circumference of a circle rolling inside another circle with a radius three times as large. Among the first to study its properties was Leonhard Euler while working on a problem in optics in 1745. The parametric equations of the cycloid with inner circle of radius r
are:
The length of the path of the deltoid is 16 r/3, and the area inside
the deltoid is 2πr^{ 2}. If a tangent is drawn to the
deltoid at some point, P, and the points where the tangent crosses
the deltoids other two branches are called points A and B,
then the length of AB equals 4r. If the deltoid's tangents
are drawn at points A and B, they will be perpendicular, and
they will intersect at a point inside the deltoid that is the 180° rotation
of point P about the center of the fixed circle. ## Related category• PLANE CURVES | ||||||

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