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Learn how to test whether a decimal number is divisible by 6 using various methods, such as summing the digits, forming alternating sums, or subtracting multiples of the last digit. See examples and explanations for each rule and its application.
The Pythagorean 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 is equal to the sum of the areas of the squares on the other two sides.
Learn about the original proof of the Pythagorean theorem invented by James A. Garfield, the 20th president of the United States. The proof appeared in print in 1876, when Garfield was a Congressman from Ohio.
Learn how to prove various identities involving trigonometric functions using geometry, algebra, calculus, and Euler's formula. The article covers elementary, angle sum, double-angle, half-angle, and sum to product identities, as well as inequalities and compositions of trig and inverse trig functions.
Learn the definition, proof, usage and history of the difference of two squares, a mathematical identity that factorizes the difference of two squared numbers. See examples, applications, generalizations and related topics in algebra, geometry, number theory and more.
Learn how to express a rational fraction as a sum of a polynomial and fractions with simpler denominators. See the basic principles, examples, methods and applications of partial fraction decomposition in algebra and calculus.
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