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If r is the inradius of a circle inscribed in a right triangle with sides a and b and hypotenuse c, then r=1/2(a+b-c). (1) A Sangaku problem dated 1803 from the Gumma ...

The Kenmotu circle is the circle passing through the six contact points of the congruent squares used in the construction of the Kenmotu point with the triangle sides. It is ...

The Bevan circle, sometimes also called the excentral circle, is the circumcircle of the excentral triangle of the reference triangle, i.e., it is the circle passing through ...

The pedal circle with respect to a pedal point P of a triangle DeltaA_1A_2A_3 is the circumcircle of the pedal triangle DeltaP_1P_2P_3 with respect to P. Amazingly, the ...

From the feet H_A, H_B, and H_C of each altitude of a triangle DeltaABC, draw lines (H_AP_A,H_AQ_A), (H_BP_B,H_BQ_B), (H_CP_C,H_CQ_C) perpendicular to the adjacent sides, as ...

The circle map is a one-dimensional map which maps a circle onto itself theta_(n+1)=theta_n+Omega-K/(2pi)sin(2pitheta_n), (1) where theta_(n+1) is computed mod 1 and K is a ...

A power of 10.

The involute of the circle was first studied by Huygens when he was considering clocks without pendula for use on ships at sea. He used the circle involute in his first ...

The circle through the cusp of the arbelos and the tangent points of the first Pappus circle, which is congruent to the two Archimedes' circles. If AB=r and AC=1, then the ...

An arrangement of overlapping circles which cover the entire plane. A lower bound for a covering using equivalent circles is 2pi/sqrt(27) (Williams 1979, p. 51).