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A magic triangle or perimeter magic triangle[1] is an arrangement of the integers from 1 to n on the sides of a triangle with the same number of integers on each side, called the order of the triangle, so that the sum of integers on each side is a constant, the magic sum of the triangle. [1][2][3][4] Unlike magic squares, there are different ...
Magic circles were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui (c. 1238–1298). It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameters are identical. One of his magic circles was constructed from the natural numbers from 1 to 33 arranged ...
We can calculate s = tan B/2 = tan (π/4 − A/2) = (1 − r) / (1 + r) from the formula for the tangent of the difference of angles. Use of s instead of r in the above formulas will give the same primitive Pythagorean triple but with a and b swapped.
Li Ye's inscribed circle in triangle:Diagram of a round town Yang Hui's magic concentric circles – numbers on each circle and diameter (ignoring the middle 9) sum to 138 Ceyuan haijing ( Chinese : 測圓海鏡 ; pinyin : Cèyuán Hǎijìng ), or Sea-Mirror of the Circle Measurements , is a collection of 692 formula and 170 problems related to ...
A 3-simplex, with barycentric subdivisions of 1-faces (edges) 2-faces (triangles) and 3-faces (body). In geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.).
The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book Xiangjie Jiuzhang Suanfa (詳解九章算法) [1] of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's Triangle" was invented by mathematician Jia Xian [2] who expounded it around 1100 AD, about 500 years before Pascal.
Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt c. 3000 to c. 300 BCE, from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for counting and solving written mathematical problems, often involving multiplication and fractions.
Pascal's theorem is the polar reciprocal and projective dual of Brianchon's theorem. It was formulated by Blaise Pascal in a note written in 1639 when he was 16 years old and published the following year as a broadside titled "Essay pour les coniques. Par B. P." [1] Pascal's theorem is a special case of the Cayley–Bacharach theorem.