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Hyperbolic law of cosines - 1st law

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more

Hyperbolic law of haversines

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more

Hyperbolic law of cosines - 2nd law

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more

Hyperbolic triangle ( length of the base)

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more

Hyperbolic triangle ( length of the altitude)

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more

Hyperbolic sector (area)

A hyperbolic sector is a region of the Cartesian plane {(x,y)} bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the hyperbola xy ... more

Hyperbolic Kepler equation

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

Radial Kepler equation

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

Hyperbolic discounting

Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a ... more

Law of cosines

The law of cosines relates the cosine of an angle to the opposite side of an arbitrary triangle and the length of the triangle’s sides.
The law ... more

Area of a triangle (by the tangent of an acute or obtuse angle of the triangle)

A triangle is a polygon with three edges and three vertices. In a scalene triangle, all sides are unequal and equivalently all angles are unequal. The area ... more

Area of a triangle (by the one side and the sines of the triangle's angles)

A triangle is a polygon with three edges and three vertices. In a scalene triangle, all sides are unequal and equivalently all angles are unequal. When the ... more

Law of tangents for the triangles

The law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.The law of ... more

Morley's trisector theorem

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral ... more

Interior perpendicular bisector of a triangle

The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly ... more

Napoleon's theorem

In geometry, Napoleon’s theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward, or all inward, ... more

Morley's trisector theorem (area)

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, ... more

Law of sines ( related to the sides of the triangle)

Law of sines is an equation relating the lengths of the sides of any shaped triangle to the sines of its angles. The law of sines can be used to compute ... more

Euler line (distance between the centroid and the orthocenter of a triangle)

In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more

Euler line (distance between the circumcenter and the orthocenter of a triangle)

In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more

Relation between inradius,exradii and sides of a right triangle

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more

Area of an arbitrary triangle

The area of an arbitrary triangle can be calculated from the two sides of the triangle and the included angle.
... more

Relation between internal bisectors of angles A, B, and C of a triangle and its sides

An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant ... more

Euler line (distance between the centroid and the circumcenter of a triangle)

In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more

Relation between the sides, the dinstances of the orthocenter from the vertices and the circumradius of a triangle

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

Radius of the incircle of a right triangle

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle ... 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

Sum of the circumradius and the inradius of a right triangle

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more

Hyperbolic paraboloid equation

The hyperbolic paraboloid (not to be confused with a hyperboloid) is a doubly ruled surface shaped like a saddle. In a suitable coordinate system, a ... more

One of the legs of a right triangle related to the inradius and the other leg.

Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). The incircle or inscribed circle of ... more

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