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The verbal equivalent is "40 is to 60 as 2 is to 3." A ratio that has integers for both quantities and that cannot be reduced any further (using integers) is said to be in simplest form or lowest terms. Sometimes it is useful to write a ratio in the form 1:x or x:1, where x is not necessarily an integer, to enable comparisons of different ...
In the second step, they were divided by 3. The final result, 4 / 3 , is an irreducible fraction because 4 and 3 have no common factors other than 1. The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30. As 120 ÷ 30 = 4, and 90 ÷ 30 = 3, one gets
For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio.
The golden ratio was called the extreme and mean ratio by Euclid, [2] ... It is in fact the simplest form of a continued fraction, alongside its reciprocal form: ...
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 are undefined , whereas if the codomain is taken to be the projectively extended real numbers , these entries take the value ∞ {\displaystyle \infty } (see division by zero ).
In this application, Størmer's theorem can be used to list all possible superparticular numbers for a given limit; that is, all ratios of this type in which both the numerator and denominator are smooth numbers. [2] These ratios are also important in visual harmony. Aspect ratios of 4:3 and 3:2 are common in digital photography, [8] and aspect ...
For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, [1] [2] when the rectangle is oriented as a "landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do ...
Common aspect ratios used in film and display images. The common film aspect ratios used in cinemas are 1.85:1 and 2.40:1. [1] Two common videographic aspect ratios are 4:3 (1. 3:1), [a] the universal video format of the 20th century, and 16:9 (1. 7:1), universal for high-definition television and European digital television.