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A famous example for lexical ambiguity is the following sentence: "Wenn hinter Fliegen Fliegen fliegen, fliegen Fliegen Fliegen hinterher.", meaning "When flies fly behind flies, then flies fly in pursuit of flies." [40] [circular reference] It takes advantage of some German nouns and corresponding verbs being homonymous. While not noticeable ...
For example, the automaton B1/S12 generates four very close approximations to the Sierpinski triangle when applied to a single live cell. The Sierpinski triangle can also be observed in the Game of Life by examining the long-term growth of an infinitely long single-cell-thick line of live cells, [ 63 ] as well as in Highlife, Seeds (B2/S) , and ...
For example, there is a near-equality close to the round number 1000 between powers of 2 and powers of 10: 2 10 = 1024 ≈ 1000 = 10 3 . {\displaystyle 2^{10}=1024\approx 1000=10^{3}.} Some mathematical coincidences are used in engineering when one expression is taken as an approximation of another.
In the zeroth-order example above, the quantity "a few" was given, but in the first-order example, the number "4" is given. A first-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a linear approximation, straight line with a slope: a polynomial of degree 1. For example:
It is a close approximation to the wrapped normal distribution, which is the circular analogue of the normal distribution. A freely diffusing angle θ {\displaystyle \theta } on a circle is a wrapped normally distributed random variable with an unwrapped variance that grows linearly in time.
[2] [3] One of the most famous opening lines, "It was the best of times, it was the worst of times", starts a sentence of 118 words [4] that draws the reader in by its contradiction; the first sentence of the novel, Yes even contains 477 words. Moby-Dick's "Call me Ishmael." is an example of a short opening sentence.
Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster that should be selected in order to form a close approximation to a straight line between two points.
An example is: = … The explanation for this seemingly remarkable coincidence was given by A. Doman in September 2023, and is a result of a sum related to Jacobi theta functions as follows: = = The first term dominates since the sum of the terms for k ≥ 2 {\displaystyle k\geq 2} total ∼ 0.0003436. {\displaystyle \sim 0.0003436.}