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James Tanton at Region One ESC. James Stuart Tanton (born August 1, 1966) is a mathematician and math educator. He is a winner of the Kidder Faculty Prize for his teaching at The St. Mark’s Math Institute, scholar at the Mathematical Association of America, [1] author of over ten books on mathematics, curriculum, and education, and creator of videos on mathematics on YouTube.
Encyclopedia of Mathematics is a 2005 encyclopedic reference work by American author James Tanton that was published by Facts-on-File of New York. [1] [2] Synopsis
All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse.
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
The isoperimetric inequality for triangles in terms of perimeter p and area T states that [13], with equality for the equilateral triangle. This is implied, via the AM–GM inequality, by a stronger inequality which has also been called the isoperimetric inequality for triangles: [14]
Here is a definition of triangle geometry from 1887: "Being given a point M in the plane of the triangle, we can always find, in an infinity of manners, a second point M' that corresponds to the first one according to an imagined geometrical law; these two points have between them geometrical relations whose simplicity depends on the more or ...
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. [ 1 ] [ 2 ] Heronian triangles are named after Heron of Alexandria , based on their relation to Heron's formula which Heron demonstrated with the example triangle of sides 13, 14, 15 and area 84 .