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The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [1] In the table below, the label "Undefined" represents a ratio If the codomain of the trigonometric functions is taken to be the real numbers these entries ...
The degree of the sum (or difference) of two polynomials is less than or equal to the greater of their degrees; that is, and . For example, the degree of is 2, and 2 ≤ max {3, 3}. The equality always holds when the degrees of the polynomials are different. For example, the degree of is 3, and 3 = max {3, 2}.
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial. which has roots and As the root of a quadratic polynomial, the golden ratio is a constructible number.
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions. Problems 21–23 are problems in completion, which in modern notation are simply subtraction problems.
In ancient China, values for π included 3.1547 (around 1 AD), (100 AD, approximately 3.1623), and 142 / 45 (3rd century, approximately 3.1556). [52] Around 265 AD, the Wei Kingdom mathematician Liu Hui created a polygon-based iterative algorithm and used it with a 3,072-sided polygon to obtain a value of π of 3.1416.
This is a list of emoticons or textual portrayals of a writer's moods or facial expressions in the form of icons. Originally, these icons consisted of ASCII art, and later, Shift JIS art and Unicode art. In recent times, graphical icons, both static and animated, have joined the traditional text-based emoticons; these are commonly known as ...