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The name Desmos came from the Greek word δεσμός which means a bond or a tie. [6] In May 2022, Amplify acquired the Desmos curriculum and teacher.desmos.com. Some 50 employees joined Amplify. Desmos Studio was spun off as a separate public benefit corporation focused on building calculator products and other math tools. [7]
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
Pythagorean theorem: It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation: [6]
Pick's theorem was included in a 1999 web listing of the "top 100 mathematical theorems", which later became used by Freek Wiedijk as a benchmark set to test the power of different proof assistants. As of 2024 [update] , Pick's theorem had been formalized and proven in only two of the ten proof assistants recorded by Wiedijk.
A more serious issue with the use of a power-of-two modulus is that the low bits have a shorter period than the high bits. Its simplicity of implementation comes from the fact that bits are never affected by higher-order bits, so the low b bits of such a generator form a modulo-2 b LCG by themselves, repeating with a period of 2 b−2.
The rule according to higher law is a practical approach to the implementation of the higher law theory that creates a bridge of mutual understanding (with regard to universal legal values) between the English-language doctrine of the rule of law, traditional for the countries of common law, and the originally German doctrine of Rechtsstaat ...
Also the angles in a hyperbolic triangle add up to less than 180° (a defect), while those on a spherical triangle add up to more than 180° (an excess). In modern terms, the defect at a vertex is a discrete version of the curvature of the polyhedral surface concentrated at that point .
In a hyperbolic triangle the sum of the angles A, B, C (respectively opposite to the side with the corresponding letter) is strictly less than a straight angle. The difference between the measure of a straight angle and the sum of the measures of a triangle's angles is called the defect of the triangle.