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A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

The point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...

Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

An axis is a line with respect to which a curve or figure is drawn, measured, rotated, etc. The most common axes encountered are commonly the mutually perpendicular Cartesian ...

The area of the shadow of a body on a plane, also called the "outer quermass."

The Euclidean plane parametrized by coordinates, so that each point is located based on its position with respect to two perpendicular lines, called coordinate axes. They are ...

The evolute of a circle is a degenerate point at the origin.

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 pedal curve of a unit circle with parametric equation x = cost (1) y = sint (2) with pedal point (x,y) is x_p = cost-ycostsint+xsin^2t (3) y_p = ...

Two figures are said to be similar when all corresponding angles are equal, and are directly similar when all corresponding angles are equal and described in the same ...