# „The solution of (1), which represents a homogeneous manifold, may be written in the form:ds^2 = \frac{d\rho^2}{1 - \kappa^2\rho^2} - \rho^2 (d\theta^2 + sin^2 \theta \; d\phi^2) + (1 - \kappa^2 \rho^2)\; c^2 d\tau^2, \qquad (2)where \kappa = \sqrt \frac{\lambda}{3}. If we consider \rho as determining distance from the origin… and \tau as measuring the proper-time of a clock at the origin, we are led to the de Sitter spherical world…“

"On Relativistic Cosmology" (1928)

Übernommen aus Wikiquote. Letzte Aktualisierung 3. Juni 2021. Geschichte
##### Howard P. Robertson
amerikanischer Mathematiker und Physiker 1903 - 1961

## Ähnliche Zitate

### „All the light which is radiated… will, after it has traveled a distance r, lie on the surface of a sphere whose area S is given by the first of the formulae (3). And since the practical procedure… in determining d is equivalent to assuming that all this light lies on the surface of a Euclidean sphere of radius d, it follows…4 \pi d^2 = S = 4 \pi r^2 (1 - \frac{K r^2}{3} + …);whence, to our approximation 4)d = r (1- \frac{K r^2}{6} + …), orr = d (1 + \frac{K d^2}{6} + …).</center“

—  Howard P. Robertson American mathematician and physicist 1903 - 1961

Geometry as a Branch of Physics (1949)

### „In the work of Vieta the analytic methods replaced the geometric, and his solutions of the quadratic equation were therefore a distinct advance upon those of his predecessors. For example, to solve the equation x^2 + ax + b = 0 he placed u + z for x. He then hadu^2 + (2z + a)u +(z^2 + az + b) = 0.He now let 2z + a = 0, whence z = -\frac{1}{2}a,and this gaveu^2 - \frac{1}{4}(a^2 - 4b) = 0.u = \pm \frac{1}{2} \sqrt{a^2 - 4b}.andx = u + z = -\frac{1}{2}a \pm \sqrt{a^2 - 4b}.</center“

—  David Eugene Smith American mathematician 1860 - 1944

Quelle: History of Mathematics (1925) Vol.2, p.449

### „Measurements which may be made on the surface of the earth… is an example of a 2-dimensional congruence space of positive curvature K = \frac{1}{R^2}… [C]onsider… a "small circle" of radius r (measured on the surface!)… its perimeter L and area A… are clearly less than the corresponding measures 2\pi r and \pi r^2… in the Euclidean plane. …for sufficiently small r (i. e., small compared with R) these quantities on the sphere are given by 1):L = 2 \pi r (1 - \frac{Kr^2}{6} + …),A = \pi r^2“

—  Howard P. Robertson American mathematician and physicist 1903 - 1961

1 - \frac{Kr^2}{12} + …
Geometry as a Branch of Physics (1949)

### „[T]he astronomical data give the number N of nebulae counted out to a given inferred "distance" d, and in order to determine the curvature… we must express N, or equivalently V, to which it is assumed proportional, in terms of d. …from the second of formulae (3) and… (4)… to the approximation here adopted, 5)V = \frac{4}{3} \pi d^2 (1 + \frac{3}{10} K d^2 + …);…plotting N against… d and comparing… with the formula (5), it should be possible operationally to determine the "curvature" K.“

—  Howard P. Robertson American mathematician and physicist 1903 - 1961

Geometry as a Branch of Physics (1949)

### „[Zuanne de Tonini] da Coi… impuned Tartaglia to publish his method, but the latter declined to do so. In 1539 Cardan wrote to Tartaglia, and a meeting was arranged at which, Tartaglia says, having pledged Cardan to secrecy, he revealed the method in cryptic verse and later with a full explanation. Cardan admits that he received the solution from Tartaglia, but… without any explanation. At any rate, the two cubics x^3 + ax^2 = c and x^3 + bx = c could now be solved. The reduction of the general cubic x^3 + ax^2 + bx = c to the second of these forms does not seem to have been considered by Tartaglia at the time of the controversy. When Cardan published his Ars Magna however, he transformed the types x^3 = ax^2 + c and x^3 + ax^2 = c by substituting x = y + \frac{1}{3}a and x = y - \frac{1}{3}a respectively, and transformed the type x^3 + c = ax^2 by the substitution x = \sqrt[3]{c^2/y}, thus freeing the equations of the term x^2. This completed the general solution, and he applied the method to the complete cubic in his later problems.“

—  David Eugene Smith American mathematician 1860 - 1944

Quelle: History of Mathematics (1925) Vol.2, p.461

### „Consider an event, for example the outburst if a nova… Suppose this event is observed from two stars in line with the nova, and suppose further that the two stars are moving uniformly with respect to each other in this line. Let the epoch at which these stars passed by each other be taken as the zero of time measurement, and let an observer A on one of the stars estimate the distance and epoch of the nova outburst to be x units of length and t units of time, respectively. Suppose the other star is moving toward the nova with velocity v relative to A. Let an observer B on the star estimate the distance and epoch of the nova outburst to be x' units of length and t' units of time, respectively. Then the Lorentz formulae, relating x' to t', arex' = \frac {x-vt}{\sqrt{1-\frac{v^2}{c^2}}}; \qquad t' = \frac {t-\frac{vx}{c^2}}{\sqrt{1-\frac{v^2}{c^2}}}These formulae are… quite general, applying to any event in line with two uniformly moving observers. If we let c become infinite then the ratio of v to c tends to zero and the formulae becomex' = x - vt; \qquad t' = t.“

—  Gerald James Whitrow British mathematician 1912 - 2000

p, 125
The Structure of the Universe: An Introduction to Cosmology (1949)

### „Vieta was the first algebraist after Ferrari to make any noteworthy advance in the solution of the biquadratic. He began with the type x^4 + 2gx^2 + bx = c, wrote it as x^4 + 2gx^2 = c - bx, added gx^2 + \frac{1}{4}y^2 + yx^2 + gy to both sides, and then made the right side a square after the manner of Ferrari. This method… requires the solution of a cubic resolvent.Descartes (1637) next took up the question and succeeded in effecting a simple solution… a method considerably improved (1649) by his commentator Van Schooten. The method was brought to its final form by Simpson“

—  David Eugene Smith American mathematician 1860 - 1944

1745
Quelle: History of Mathematics (1925) Vol.2, p.469

### „The discovery of Hippocrates amounted to the discovery of the fact that from the relation(1)\frac{a}{x} = \frac{x}{y} = \frac{y}{b}it follows that(\frac{a}{x})^3 = [\frac{a}{x} \cdot \frac{x}{y} \cdot \frac{y}{b} =] \frac{a}{b}and if a = 2b, [then (\frac{a}{x})^3 = 2, and]a^3 = 2x^3.The equations (1) are equivalent [by reducing to common denominators or cross multiplication] to the three equations(2)x^2 = ay, y^2 = bx, xy = ab[or equivalently…y = \frac{x^2}{a}, x = \frac{y^2}{b}, y = \frac{ab}{x} ]Doubling the Cubethe 2 solutions of Menaechmusand the solutions of Menaechmus described by Eutocius amount to the determination of a point as the intersection of the curves represented in a rectangular system of Cartesian coordinates by any two of the equations (2).Let AO, BO be straight lines placed so as to form a right angle at O, and of length a, b respectively. Produce BO to x and AO to y.The first solution now consists in drawing a parabola, with vertex O and axis Ox, such that its parameter is equal to BO or b, and a hyperbola with Ox, Oy as asymptotes such that the rectangle under the distances of any point on the curve from Ox, Oy respectively is equal to the rectangle under AO, BO i. e. to ab. If P be the point of intersection of the parabola and hyperbola, and PN, PM be drawn perpendicular to Ox, Oy, i. e. if PN, PM be denoted by y, x, the coordinates of the point P, we shall have\begin{cases}y^2 = b. ON = b. PM = bx\\ and\\ xy = PM. PN = ab\end{cases}whence\frac{a}{x} = \frac{x}{y} = \frac{y}{b}.In the second solution of Menaechmus we are to draw the parabola described in the first solution and also the parabola whose vertex is O, axis Oy and parameter equal to a.“

—  Thomas Little Heath British civil servant and academic 1861 - 1940

The point P where the two parabolas intersect is given by<center>$\begin{cases}y^2 = bx\\x^2 = ay\end{cases}$</center>whence, as before,<center>$\frac{a}{x} = \frac{x}{y} = \frac{y}{b}.$</center>
Apollonius of Perga (1896)

### „[T]he formalist school, of whom the most eminent representative is Hilbert, have concentrated on the propositions of mathematics, such as '2 + 2 = 4'. They have pronounced these to be meaningless formulae to be manipulated according to arbitrary rules, and they hold that mathematical knowledge consists in knowing what formulae can be derived from what others consistently with the rules…. for example…'2' is a meaningless mark occurring in these meaningless formulae. But… '2' occurs not only in '2 + 2 = 4', but also in 'It is 2 miles to the station', which is not a meaningless formulae, but a significant proposition, in which '2' cannot conceivably be a meaningless mark.“

—  Frank P. Ramsey British mathematician, philosopher 1903 - 1930

The Foundations of Mathematics (1925)

### „Fermat died with the belief that he had found a long-sought-for law of prime numbers in the formula 2^{2^n} + 1 = a prime, but he admitted that he was unable to prove it rigorously. The law is not true, as was pointed out by Euler in the example 2^{2^5} + 1 = 4,294,967,297 = 6,700,417 times 641. The American lightning calculator Zerah Colburn, when a boy, readily found the factors but was unable to explain the method by which he made his marvellous mental computation.“

—  Florian Cajori, buch A History of Mathematics

Quelle: A History of Mathematics (1893), p. 180; also cited in Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914) pp. 156-157. https://books.google.com/books?id=G0wtAAAAYAAJ&pg=PA156

### „There always comes a time in history when the person who dares to say that 2+2=4 is punished by death.“

—  Albert Camus, buch The Plague

The Plague (1947)
Kontext: There always comes a time in history when the person who dares to say that 2+2=4 is punished by death. And the issue is not what reward or what punishment will be the outcome of that reasoning. The issue is simply whether or not 2+2=4.

### „U don't have 2 be rich2 be my girlU don't have 2 be cool2 rule my worldAin't no particular sign I'm more compatible withI just want your extra time and yourKiss.“

—  Prince American pop, songwriter, musician and actor 1958 - 2016

Kiss
Song lyrics, Parade Under the Cherry Moon (1986)

### „Women not girls rule my worldI said they rule my worldAct your age, mama (not your shoe size)Not your shoe sizeMaybe we could do the twirlU don't have 2 watch Dynasty2 have an attitudeU just leave it all up 2 meMy love will be your foodYeah.U don't have 2 be rich2 be my girlU don't have 2 be cool2 rule my worldAin't no particular sign I'm more compatible withI just want your extra time and yourKiss.“

—  Prince American pop, songwriter, musician and actor 1958 - 2016

Kiss
Song lyrics, Parade Under the Cherry Moon (1986)

### „I never meant 2 cause u any sorrowI never meant 2 cause u any painI only wanted 2 one time see u laughingI only wanted 2 see u laughing in the purple rain.“

—  Prince American pop, songwriter, musician and actor 1958 - 2016

Purple Rain
Song lyrics, Purple Rain (1984)

### „Two key rules of Third World travel: 1. Never run out of whiskey. 2. Never run out of whiskey.“

—  P. J. O'Rourke American journalist 1947

All the Trouble in the World (1994)

### „If an angel were ever to tell us anything of his philosophy I believe many propositions would sound like 2 times 2 equals 13.“

—  Georg Christoph Lichtenberg German scientist, satirist 1742 - 1799

B 44
Aphorisms (1765-1799), Notebook B (1768-1771)

### „Art is (1) a messenger of discontent, yet (2) no teacher of new ideals, but rather (3) an inspiration to each it touches, himself to turn creator of a world-more-ideal.“

—  Edgar A. Singer, Jr. American philosopher 1873 - 1954

Singer, Edgar A. "Esthetic and the Rational Ideal. II." The Journal of Philosophy 23.10 (1926): 258-268; Partly cited in: William Gerber. Anatomy of what We Value Most, Rodopi, 1997, p. 55

### „Proposition 11. The diameter of the moon is less than 2/45ths, but greater than 1/30th of the distance of the centre of the moon from our eye.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

### „A new point is determined in Euclidean Geometry exclusively in one of the three following ways:Having given four points A, B, C, D, not all incident on the same straight line, then(1) Whenever a point P exists which is incident both on (A, B) and on (C, D), that point is regarded as determinate.(2) Whenever a point P exists which is incident both on the straight line (A, B) and on the circle C(D), that point is regarded as determinate.(3) Whenever a point P exists which is incident on both the circles A(B), C(D), that point is regarded as determinate.The cardinal points of any figure determined by a Euclidean construction are always found by means of a finite number of successive applications of some or all of these rules (1), (2) and (3). Whenever one of these rules is applied it must be shown that it does not fail to determine the point. Euclid's own treatment is sometimes defective as regards this requisite.In order to make the practical constructions which correspond to these three Euclidean modes of determination, correponding to (1) the ruler is required, corresponding to (2) both ruler and compass, and corresponding to (3) the compass only.…it is possible to develop Euclidean Geometry with a more restricted set of postulations. For example it can be shewn that all Euclidean constructions can be carried out by means of (3) alone…“

—  E. W. Hobson British mathematician 1856 - 1933

Quelle: Squaring the Circle (1913), pp. 7-8

### „The words "routine analyses" are used to denote the analyses performed by laboratories, frequently attached to industrial plants, and distinguished by the following characteristics: (1) All the analyses or measurements of the same kind, for example, are designed to measure the sugar content in beets or to determine the coordinates of a star. (2) The analyses are carried out day after day using the same methods and the same instruments. (3) While all the analyses are of the same kind, the quantity n varies from time to time, where n represents some small number, 2, 3, 4, 5.“

—  Jerzy Neyman Polish statistician 1894 - 1981

p. 46 of "On a statistical problem arising in routine analyses and in sampling inspections of mass production." http://www.jstor.org/stable/2235624 The Annals of Mathematical Statistics 12, no. 1 (1941): 46–76.