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Both of these matrices are unimodular, arbitrary products remain unimodular, and result in a matrix of the form + + = giving the precise value of the continued fraction. As all of the matrix entries are integers, this matrix belongs to the projective modular group P S L ( 2 , Z ) . {\displaystyle PSL(2,\mathbb {Z} ).}
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
The results of that example may be used to simulate a fractional factorial experiment using a half-fraction of the original 2 4 = 16 run design. The table shows the 2 4-1 = 8 run half-fraction experiment design and the resulting filtration rate, extracted from the table for the full 16 run factorial experiment.
One of the simplest tests for convergence of a series, applicable to all series, is the vanishing condition or th-term test: If , then the series diverges; if =, then the test is inconclusive.
In computer graphics, polynomials can be used to approximate complicated plane curves given a few specified points, for example the shapes of letters in typography. This is usually done with Bézier curves , which are a simple generalization of interpolation polynomials (having specified tangents as well as specified points).
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
where the word premier, French for "first", can be read. Braille was based on a tactile code, now known as night writing, developed by Charles Barbier. (The name "night writing" was later given to it when it was considered as a means for soldiers to communicate silently at night and without a light source, but Barbier's writings do not use this term and suggest that it was originally designed ...
Within the first fraction of a second of the universe's existence, the four fundamental forces had separated. As the universe continued to cool from its inconceivably hot state, various types of subatomic particles were able to form in short periods of time known as the quark epoch, the hadron epoch, and the lepton epoch. Together, these epochs ...