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Law of cotangents (in term of tangents)

In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. ... more

Perimeter of an Equilateral polygon

An equilateral polygon is a polygon which has all sides of the same length. A perimeter of an equilateral polygon is a path that surrounds it in two ... more

Perimeter of a rhombus

A rhombus is a simple (non-self-intersecting) quadrilateral all of whose four sides have the same length. A perimeter of a rhombus is a path that surrounds ... more

Perimeter of a Square

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles). A perimeter of a ... more

Perimeter of a Regular polygon

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may ... more

Perimeter of Rectangle

A rectangle is any quadrilateral with four right angles. A convex quadrilateral is a rectangle if and only if it is any one of the following:
an ... more

Area of an arbitrary triangle related to the incircle radius

The area related to the semi perimeter of the triangle and the radius of the inscribed circle.

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Altitude of a triangle

The altitude of a triangle is the distance from a vertex perpendicular to the opposite side. There is a relation between the altitude and the sides of the ... more

Thermal resistance due to fouling deposits (general)

Often during their use, heat exchangers collect a layer of fouling on the surface which, in addition to potentially contaminating a stream, reduces the ... more

Wetted perimeter

The wetted perimeter is the perimeter of the cross sectional area that is “wet”. The term wetted perimeter is common in civil engineering, ... more

Area of rhombus (circumscribed)

Rhombus is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length. The can be calculated by the semi perimeter and the ... more

Area of a regular inscribed n-gon (polygon)

The area of a regular inscribed n-gon (polygon) can be computed in terms of the radius R of its circumscribed circle and its perimeter p

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Length of the perimeter of a circular sector

Circular arc is a segment of a circle. A circular sector or circle sector is the portion of a disk enclosed by two radii and an arc, where the smaller area ... 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 medians)

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

Length of the internal bisector of a triangle

An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half. The three angle bisectors intersect in a ... more

Area of a triangle (Heron's formula)

In geometry, Heron’s formula (sometimes called Hero’s formula), named after Hero of Alexandria, gives the area of a triangle by requiring no ... more

2nd medians' theorem

Relates the projection of a median and the sides of an arbitrary triangle

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Area of a triangle (Heron's formula) - alternative version

In geometry, Heron’s formula (sometimes called Hero’s formula), named after Hero of Alexandria, gives the area of a triangle by requiring no ... more

Length of the medians of a triangle

Median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each ... more

Area of an Isosceles triangle ( by its sides)

An isosceles triangle is a triangle that has two sides of equal length. The area of the isosceles triangle can be calculated by the lengths of the sides.

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Pythagorean theorem (arbitrary triangle - acute angle)

Generalization of the Pythagorean theorem for the side opposite of the acute angle of an arbitrary triangle

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Pythagorean theorem (arbitrary triangle - obtuse angle)

Generalization of the Pythagorean theorem for the side opposite of the obtuse angle of an arbitrary triangle

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Length of a side of an inscribed square in a triangle

Every acute triangle has three inscribed squares (squares in its interior such that all four of a square’s vertices lie on a side of the triangle, so ... 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

Tangent function

The trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its ... more

Cotangent function

The trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its ... more

Cosine function

The trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its ... more

Sine function

The trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its ... more

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