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In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem [1] or the upside down Pythagorean theorem [2]) is as follows: [3] Let A, B be the endpoints of the hypotenuse of a right triangle ABC. Let D be the foot of a perpendicular dropped from C, the vertex of the right angle, to the hypotenuse. Then
The proof proceeds by induction on , and uses the Inverse Pythagorean Theorem, which states that: 1 a 2 + 1 b 2 = 1 h 2 {\displaystyle {\frac {1}{a^{2}}}+{\frac {1}{b^{2}}}={\frac {1}{h^{2}}}} where a {\displaystyle a} and b {\displaystyle b} are the cathetes and h {\displaystyle h} is the height of a right triangle.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.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.
Louisiana students Ne’Kiya Jackson and Calcea Johnson wowed their teachers in 2022 when they discovered a new way to prove the 2000-year-old Pythagorean theorem in response to a bonus question ...
In a right triangle, the sum of the reciprocals of the squares of the altitudes from the legs (equivalently, of the squares of the legs themselves) equals the reciprocal of the square of the altitude from the hypotenuse (the inverse Pythagorean theorem).
Bhaskaracharya proof of the pythagorean Theorem. Some of Bhaskara's contributions to mathematics include the following: A proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms to get a 2 + b 2 = c 2. [21] In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations ...
Trigonometric functions of inverse trigonometric functions are tabulated below. A quick way to derive them is by considering the geometry of a right-angled triangle, with one side of length 1 and another side of length , then applying the Pythagorean theorem and definitions of the
Inverse eigenvalues theorem (linear algebra) Inverse function theorem (vector calculus) Ionescu-Tulcea theorem (probability theory) Isomorphism extension theorem (abstract algebra) Isomorphism theorem (abstract algebra) Isoperimetric theorem (curves, calculus of variations)