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Semi-Minor Axis - Ellipse

In geometry, the semi-minor axis (also semiminor axis) is a line segment associated with most conic sections (that is, with ellipses and hyperbolas) that ... more

Rhombic triacontahedron Volume

Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. The ratio of the long diagonal to the ... more

Rhombic triacontahedron Area

Rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It has 60 edges and 32 vertices of two types. The ratio of the long diagonal to the ... more

Center of mass of a uniform trapezoid

Trapezoid is a convex quadrilateral with only one pair of parallel sides. The parallel sides are called the bases of the trapezoid and the other two sides ... more

Dodecahedron regular (inscribed sphere radius

A regular dodecahedron is a polyhedron composed of 12 regular pentagonal faces, with three meeting at each vertex. It has 20 vertices, 30 edges and 160 ... more

Regular Dodecahedron ( midscribed sphere radius)

A regular dodecahedron is a polyhedron composed of 12 regular pentagonal faces, with three meeting at each vertex. It has 20 vertices, 30 edges and 160 ... more

Regular Dodecahedron ( circumscribed sphere radius

A regular dodecahedron is a polyhedron composed of 12 regular pentagonal faces, with three meeting at each vertex. It has 20 vertices, 30 edges and 160 ... more

Menzerath's Law

Menzerath’s law, or Menzerath–Altmann law (named after Paul Menzerath and Gabriel Altmann), is a linguistic law according to which the increase of a ... more

Regular Icosahedron ( circumscribed sphere radius)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Regular Icosahedron ( midscribed sphere radius)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Regular Icosahedron ( inscribed sphere radius)

An icosahedron is a polyhedron with 20 triangular faces, 30 edges and 12 vertices. A regular icosahedron has 20 identical equilateral faces, with five of ... more

Theorem of internal triangle's bisector

The bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle

... more

Euler's quadrilateral theorem

In any convex quadrilateral the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals plus four times the square of ... more

Normal segment for a given line

The normal segment for a given line is defined to be the line segment drawn from the origin perpendicular to the line. This segment joins the origin with ... more

Right triangle altitude theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the ... more

Ceva's theorem (lines from vertices to the opposite sides of a triangle)

Ceva’s theorem is a theorem about triangles in Euclidean plane geometry. Given a triangle ABC, let the lines AO, BO and CO ... more

Menelaus' theorem ( transversal line passes inside triangle )

Menelaus’ theorem, named for Menelaus of Alexandria, is a theorem about triangles in plane geometry. Given a triangle ABC, ... more

Block and tackle - effort required to raise a given weight

A block and tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads.The formula used ... more

Length of internal bisector of an angle in triangle in relation to the opposite segments

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector. If the internal ... more

Tractrix

Tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a ... more

Block and tackle - efficiency approximation - with friction factor

A block and tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads.A more precise ... more

Stewart's Theorem

Stewart’s theorem yields a relation between the length of the sides of the triangle and the length of a cevian of the triangle. A cevian is any line ... more

Stewart's Theorem ( for triangle's bisectors)

Stewart’s theorem yields a relation between the length of the sides of the triangle and the length of a cevian of the triangle. A cevian is any line ... more

Cissoid of Diocles (Cartesian coordinates)

The Cissoid of Diocles is a cubic plane curve member of the conchoid of de Sluze family of curves and in form it resembles a tractrix.( Tractix is the ... more

Sum of the ratios on the three altitudes of the distance of the orthocenter from the vertex to the length of the altitude

Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more

Sum of the ratios on the three altitudes of the distance of the orthocenter from the base to the length of the altitude

Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more

Tractrix (General formula-cartesian coordinates)

Tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a ... more

Area of a Cylinder

A cylinder is a geometric shape, that its surface is forming by the points at a fixed distance from a given line segment, the axis of the cylinder. The ... more

Semi-Major Axis - Ellipse

In geometry, the major axis of an ellipse is the longest diameter: a line (line segment) that runs through the center and both foci, with ends at the ... more

Kepler's equation - y coordinate

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.

It was first ... more

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