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The primary square is obtained by rotating the root square counter-clockwise by 90 degrees, and replacing the numbers. The resulting square is an associative magic square, in which every pair of numbers symmetrically opposite to the center sum up to the same value, 26. For e.g., 16+10, 3+23, 6+20, etc.
The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of can be found using difference of two squares: (since ) Therefore, the linear factors are and . Since the two factors found by this method are complex conjugates, we can use this in ...
Addition principle. 5+0=5 illustrated with collections of dots. In combinatorics, the addition principle[1][2] or rule of sum[3][4] is a basic counting principle. Stated simply, it is the intuitive idea that if we have A number of ways of doing something and B number of ways of doing another thing and we can not do both at the same time, then ...
Complex number. A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i2 = −1. In mathematics, a complex number is an element of a number system ...
This image actually shows two Karnaugh maps: for the function ƒ, using minterms (colored rectangles) and for its complement, using maxterms (gray rectangles). In the image, E () signifies a sum of minterms, denoted in the article as . The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions.
Geometric series. The geometric series 1/4 + 1/16 + 1/64 + 1/256 + ... shown as areas of purple squares. Each of the purple squares has 1/4 of the area of the next larger square (1/2× 1/2 = 1/4, 1/4×1/4 = 1/16, etc.). The sum of the areas of the purple squares is one third of the area of the large square. Another geometric series (coefficient ...
Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 + 14 = 16). Thus 16 × 5 = 80 is twice the sum.
Hypotenuse. A right-angled triangle and its hypotenuse. In geometry, a hypotenuse is the side of a right triangle opposite the right angle. [1] It is the longest side of any such triangle; the two other shorter sides of such a triangle are called catheti or legs. The length of the hypotenuse can be found using the Pythagorean theorem, which ...