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The radial curve of the deltoid x = 1/3a[2cost+cos(2t)] (1) y = 1/3a[2sint-sin(2t)] (2) with pedal point (x_0,y_0) is x_p = 1/6[3x+cost+3xcost-cos(2t)-3ysint] (3) y_p = ...

The angle obtained by drawing the auxiliary circle of an ellipse with center O and focus F, and drawing a line perpendicular to the semimajor axis and intersecting it at A. ...

A quantity defined for a conic section which can be given in terms of semimajor a and semiminor axes b. interval curve e e=0 circle 0 0<e<1 ellipse sqrt(1-(b^2)/(a^2)) e=1 ...

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...

A 1-cusped epicycloid has b=a, so n=1. The radius measured from the center of the large circle for a 1-cusped epicycloid is given by epicycloid equation (◇) with n=1 so r^2 = ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

A strophoid of a circle with the pole O at the center of the circle and the fixed point P on the circumference of the circle. Freeth (1878, pp. 130 and 228) described this ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...

The Hammer-Aitoff equal-area projection, also called the Hammer projection, is a map projection that is a modification of the Lambert azimuthal equal-area projection. It ...