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The product operator for the product of a sequence is denoted by the capital Greek letter pi Π (in analogy to the use of the capital Sigma Σ as summation symbol). [1] For example, the expression ∏ i = 1 6 i 2 {\displaystyle \textstyle \prod _{i=1}^{6}i^{2}} is another way of writing 1 ⋅ 4 ⋅ 9 ⋅ 16 ⋅ 25 ⋅ 36 {\displaystyle 1 ...
Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin( α + β ) = sin α cos β + cos α sin ...
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form (row value, column value). [4] One can similarly define the Cartesian product of n sets, also known as an n-fold Cartesian product, which can be represented by an n-dimensional array, where each element is an n-tuple.
The Comptometer was the first commercially successful key-driven mechanical calculator, patented in the United States by Dorr Felt in 1887.. A key-driven calculator is extremely fast because each key adds or subtracts its value to the accumulator as soon as it is pressed and a skilled operator can enter all of the digits of a number simultaneously, using as many fingers as required, making ...
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [1] [2] [3] On an expression or formula calculator, one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.
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Comparison of the convergence of the Wallis product (purple asterisks) and several historical infinite series for π. S n is the approximation after taking n terms. Each subsequent subplot magnifies the shaded area horizontally by 10 times. (click for detail) The Wallis product is the infinite product representation of π: