Search results
Results from the WOW.Com Content Network
The Pythagorean theorem has at least 370 known proofs. [1]In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. [a] [2] [3] The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
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.
The theorem that the base angles of an isosceles triangle are equal appears as Proposition I.5 in Euclid. [51] This result has been called the pons asinorum (the bridge of asses) or the isosceles triangle theorem. Rival explanations for this name include the theory that it is because the diagram used by Euclid in his demonstration of the result ...
Two-square theorem — Denote the number of divisors of as (), and write () for the number of those divisors with . Let n = 2 f p 1 r 1 p 2 r 2 ⋯ q 1 s 1 q 2 s 2 ⋯ {\displaystyle n=2^{f}p_{1}^{r_{1}}p_{2}^{r_{2}}\cdots q_{1}^{s_{1}}q_{2}^{s_{2}}\cdots } where p i ≡ 1 mod 4 , q i ≡ 3 mod 4 {\displaystyle p_{i}\equiv 1{\bmod {4}},\ q_{i ...
In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases ...
Thales' theorem, named after Thales of Miletus states that if A, B, and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. Cantor supposed that Thales proved his theorem by means of Euclid Book I, Prop. 32 after the manner of Euclid Book III, Prop. 31. [15] [16]
We love getting advice from grandma, but some of her cleaning tricks may be outdated. We asked a cleaning pro to share the top tips to ditch once and for all.
Menelaus's theorem, case 1: line DEF passes inside triangle ABC. In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A ...