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- He is usually credited with the proof of the Pythagorean theorem using similar triangles.
- videos) proves an amusing (but trivial) version of the Pythagorean theorem: construct a (2D) teapot on each side of a right triangle and the area of the teapot on the hypotenuse is equal to the sum of the areas of the teapots on the other two sides.
- Regarding the direct application of the Gou Gu Theorem, which is precisely the Chinese version of the Pythagorean Theorem, the book divides it into four main categories: Gou Gu mutual seeking, Gou Gu integer, Gou Gu dual capacity, Gou Gu similar.
- Equivalently, the law of cosines may be used to first compute the length of the spoke as projected on the wheel's plane (as illustrated in the diagram), followed by an application of the Pythagorean theorem.
- , calculated using the relativistic version of the Pythagorean theorem which has a different sign for the space and time dimensions.
- Another important contribution Thabit made to geometry was his generalization of the Pythagorean theorem, which he extended from special right triangles to all triangles in general, along with a general proof.
- The left-hand picture below is an example of a historic visual proof of the Pythagorean theorem in the case of the (3,4,5) triangle.
- The Pythagorean theorem states how to determine when a triangle is a right triangle.
- The Pythagorean theorem can be used as the basis of methods of constructing right angles.
- It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance.
- Statistical manifolds corresponding to Bregman divergences are flat manifolds in the corresponding geometry, allowing an analog of the Pythagorean theorem (which holds for squared Euclidean distance) to be used for linear inverse problems in inference by optimization theory.
- Where the angle is a right angle, also known as the hypotenuse-leg (HL) postulate or the right-angle-hypotenuse-side (RHS) condition, the third side can be calculated using the Pythagorean theorem thus allowing the SSS postulate to be applied.
- The area formula [...] in terms of side length "a" can be derived directly using the Pythagorean theorem or using trigonometry.
- In this formula the angle at [...] is opposite to the side [...]. This theorem can be proved by dividing the triangle into two right ones and using the Pythagorean theorem.
© dict.cc English-German dictionary 2023
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