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The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
1, 3, 21, and 55 are the only triangular Fibonacci numbers, which was conjectured by Vern Hoggatt and proved by Luo Ming. [52] No Fibonacci number can be a perfect number. [53] More generally, no Fibonacci number other than 1 can be multiply perfect, [54] and no ratio of two Fibonacci numbers can be perfect. [55]
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 1 : 0. {\displaystyle 1:0.}
In 1991, the thomson (symbol: Th) was proposed as a unit to measure mass-to-charge ratio in mass spectrometry in his honour. [55] J J Thomson Avenue, on the University of Cambridge's West Cambridge site, is named after Thomson. [56] The Thomson Medal Award, sponsored by the International Mass Spectrometry Foundation, is named after Thomson. [57]
The Parker square, named after recreational mathematician Matt Parker, [55] is an attempt to create a 3 × 3 magic square of squares — a prized unsolved problem since Euler. [56] Discovered in 2016, the Parker square is a trivial semimagic square, since it uses some numbers more than once, and the diagonal 23 2 + 37 2 + 47 2 sums to 4107 ...
A ratio is often converted to a fraction when it is expressed as a ratio to the whole. In the above example, the ratio of yellow cars to all the cars on the lot is 4:12 or 1:3. We can convert these ratios to a fraction, and say that 4 / 12 of the cars or 1 / 3 of the cars in the lot are yellow.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
This is a simplified view of isotope dilution but it illustrates the method's salient features. A more complex situation arises when the distinction between marked and unmarked fish becomes fuzzy. This can occur, for example, when the lake already contains a small number of marked fish from previous field experiments; and vice versa, where the ...