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A point where a stable and an unstable separatrix (invariant manifold) from the same fixed point or same family intersect. Therefore, the limits lim_(k->infty)f^k(X) and ...

The first and second isodynamic points of a triangle DeltaABC can be constructed by drawing the triangle's angle bisectors and exterior angle bisectors. Each pair of ...

The 60 Pascal lines of a hexagon inscribed in a conic intersect three at a time through 20 Steiner points, and also three at a time in 60 points known as Kirkman points. Each ...

The approximation for pi given by pi approx sqrt((40)/3-2sqrt(3)) (1) = 1/3sqrt(120-18sqrt(3)) (2) = 3.141533.... (3) In the above figure, let OA=OF=1, and construct the ...

Consider a convex pentagon and extend the sides to a pentagram. Externally to the pentagon, there are five triangles. Construct the five circumcircles. Each pair of adjacent ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

A right angle is an angle equal to half the angle from one end of a line segment to the other. A right angle is pi/2 radians or 90 degrees. A triangle containing a right ...

Two or more lines which have no intersections but are not parallel, also called agonic lines. Since two lines in the plane must intersect or be parallel, skew lines can exist ...

A four-sided quadrilateral not contained in a plane. The lines connecting the midpoints of opposite sides of a skew quadrilateral intersect (and bisect) each other (Steinhaus ...

A spherical sector is a solid of revolution enclosed by two radii from the center of a sphere. The spherical sector may either be "open" and have a conical hole (left figure; ...