Quotes about trigonometry

A collection of quotes on the topic of trigonometry, algebra, geometry, use.

Quotes about trigonometry

“The development of Indian trigonometry, based on sine as against chord of the Greeks, a necessity for astronomical calculations with his own concise notation which expresses the full sine table in just one couplet for easy remembrance. One of the two methods suggested by him for the sine table is based on the property that the second order sine differences were proportional to sines themselves.”

Aryabhata (476–550) Indian mathematician-astronomer

In, P.245.
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures

“All the geography, trigonometry, and arithmetic in the world are useless unless you learn to think for yourself. No school teaches you that. It's not on the curriculum.”

Carlos Ruiz Zafón book Marina

Source: Marina

World, School, Thinking, Learning

“Mathematics, trigonometry, chemistry, psychoanalysis, music, and what not have been related to cubism to give it an easier interpretation. All this has been pure literature, not to say nonsense, which brought bad results, blinding people with theories. Cubism has kept itself within the limits and limitations of painting, never pretending to go beyond it.”

Pablo Picasso (1881–1973) Spanish painter, sculptor, printmaker, ceramicist, and stage designer

As quoted by Marius de Zayas, in 'The Arts', New York, May 1923
1920s, The Arts', New York, May 1923

People, Music, Literature, Mathematics

“Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 http://books.google.com/books?id=SYJsAAAAMAAJ& (1902) <br class="br">Context: In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.

Problem

“She can tell you the height of the attacker from the trigonometry of the blood spatter, while I'm fuzzy on what trigonometry is.”

Ilona Andrews American husband-and-wife novelist duo

Source: Magic Slays

“A surprise trigonometry quiz that everyone in class fails? Must be in the Lord’s plan to give us challenges.”

Nicholas Sparks book A Walk to Remember

Source: A Walk to Remember

“[wrote_the_exam]What keeps me awake at night: wondering whether human species is just too stupid to figure out the Universe. I just wonder. I lose sleep over that. Because we define ourselves as intelligent— because we made up the test to say that. And we sit alone at the top of the intelligence chart because we invented the exam, and all the other species of life on Earth are not. So who's to say that the first species (us) to be intelligent (us) has just enough intelligence to actually decode everything that's decodable in the Cosmos? […] Think of the next closest thing to us, the bonobo chimp— 98½% identical DNA, yet you cannot teach them trigonometry, they have no concept of it. So if that's only 1½% difference in our DNA— and so imagine 1½% beyond us, rather than below us, in intelligence. […] Their toddlers would be talking about things that would completely confound us.”

Neil deGrasse Tyson (1958) American astrophysicist and science communicator

Nerdist podcast, Episode #489 http://www.nerdist.com/2014/03/nerdist-podcast-neil-degrasse-tyson-returns-again/ (2014-04) <br class="br">2010s

Life, Stupidity, Imagination, Intelligence

“I had one experience which gave me some slant on the way large organizations run. I was not allowed to take spherical trigonometry because I'd sprained my ankle. Because I'd sprained my ankle I had an incomplete in gym, phys ed. And the rule was that if you had an incomplete in anything, you were not allowed to take an overload. I argued with some clerical person in the administration office, and was stopped there. It's an experience which I've remembered since, and advised people not to be stopped at the first point.”

William Shockley (1910–1989) American physicist and inventor

Interview in 1974, quoted at "William Shockley" profile at PBS http://www.pbs.org/transistor/album1/shockley/index.html

People, Way, Personality

“My specific… object has been to contain, within the prescribed limits, the whole of the student's course, from the confines of elementary algebra and trigonometry, to the entrance of the highest works on mathematical physics. A learner who has a good knowledge of the subjects just named, and who can master the present treatise, taking up elementary works on conic sections, application of algebra to geometry, and the theory of equations, as he wants them, will, I am perfectly sure, find himself able to conquer the difficulties of anything he may meet with; and need not close any book of Laplace, Lagrange, Legendre, Poisson, Fourier, Cauchy, Gauss, Abel, Hindenburgh and his followers. or of any one of our English mathematicians, under the idea that it is too hard for him.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Preface, p. iii
The Differential and Integral Calculus (1836)

Books, Mathematics, Idea, Knowledge

“We are so accustomed to hear arithmetic spoken of as one of the three fundamental ingredients in all schemes of instruction, that it seems like inquiring too curiously to ask why this should be. Reading, Writing, and Arithmetic—these three are assumed to be of co-ordinate rank. Are they indeed co-ordinate, and if so on what grounds?
In this modern “trivium” the art of reading is put first. Well, there is no doubt as to its right to the foremost place. For reading is the instrument of all our acquisition. It is indispensable. There is not an hour in our lives in which it does not make a great difference to us whether we can read or not. And the art of Writing, too; that is the instrument of all communication, and it becomes, in one form or other, useful to us every day. But Counting—doing sums,—how often in life does this accomplishment come into exercise? Beyond the simplest additions, and the power to check the items of a bill, the arithmetical knowledge required of any well-informed person in private life is very limited. For all practical purposes, whatever I may have learned at school of fractions, or proportion, or decimals, is, unless I happen to be in business, far less available to me in life than a knowledge, say, of history of my own country, or the elementary truths of physics. The truth is, that regarded as practical arts, reading, writing, and arithmetic have no right to be classed together as co-ordinate elements of education; for the last of these is considerably less useful to the average man or woman not only than the other two, but than 267 many others that might be named. But reading, writing, and such mathematical or logical exercise as may be gained in connection with the manifestation of numbers, have a right to constitute the primary elements of instruction. And I believe that arithmetic, if it deserves the high place that it conventionally holds in our educational system, deserves it mainly on the ground that it is to be treated as a logical exercise. It is the only branch of mathematics which has found its way into primary and early education; other departments of pure science being reserved for what is called higher or university instruction. But all the arguments in favor of teaching algebra and trigonometry to advanced students, apply equally to the teaching of the principles or theory of arithmetic to schoolboys. It is calculated to do for them exactly the same kind of service, to educate one side of their minds, to bring into play one set of faculties which cannot be so severely or properly exercised in any other department of learning. In short, relatively to the needs of a beginner, Arithmetic, as a science, is just as valuable—it is certainly quite as intelligible—as the higher mathematics to a university student.”

Joshua Girling Fitch (1824–1903) British educationalist

Source: Lectures on Teaching, (1906), pp. 267-268.

Life, Truth, Education, School

“To give here an elaborate account of Pappus would be to create a false impression. His work is only the last convulsive effort of Greek geometry which was now nearly dead and was never effectually revived. It is not so with Ptolemy or Diophantus. The trigonometry of the former is the foundation of a new study which was handed on to other nations indeed but which has thenceforth a continuous history of progress. Diophantus also represents the outbreak of a movement which probably was not Greek in its origin, and which the Greek genius long resisted, but which was especially adapted to the tastes of the people who, after the extinction of Greek schools, received their heritage and kept their memory green. But no Indian or Arab ever studied Pappus or cared in the least for his style or his matter. When geometry came once more up to his level, the invention of analytical methods gave it a sudden push which sent it far beyond him and he was out of date at the very moment when he seemed to be taking a new lease of life.”

James Gow (scholar) (1854–1923) scholar

p, 125
A Short History of Greek Mathematics (1884)

Life, People, School, History

“For four or five centuries, Islam was the most brilliant civilization in the Old World. (…) At its higher level the golden age of Muslim civilization was both an immense scientific success and a exceptional revival of ancient philosophy. These was not its only triumphs; literature was another: but they eclipse the rest. First, science: it was there that the Saracens (…) made the most original contributions. These, in brief, were nothing less than trigonometry and algebra (with its significantly Arab name). (…) Equally distinguished were Islam's mathematical geographers, its astronomical observatories and instruments (…). The Muslims also deserve high marks for optics, for chemistry (…) and for pharmacy. More than half the remedies and healing aids used by the West came from Islam (…). Muslim medical skill was incontestable. (…) In the field of philosophy, what took place was rediscovery - a return, essentially of the peripatetic philosophy. The scope of this rediscovery, however, was not limited to copying and handling on, valuable as that undoubtely was. It also involved continuing, elucidating and creating.”

Fernand Braudel (1902–1985) French historian and a leader of the Annales School

A History of Civilizations , Penguin, 1995, p. 73-81

Age, World, Literature, Mathematics

“The second part of the book… contains an exposition of the first principles of the theory of complex quantities; hitherto, the very elements of this theory have not been easily accessible to the English student, except recently in Prof. Chrystal's excellent treatise on Algebra. The subject of Analytical Trigonometry has been too frequently presented to the student in the state in which it was left by Euler, before the researches of Cauchy, Abel, Gauss, and others, had placed the use of imaginary quantities, and especially the theory of infinite series and products, where real or complex quantities are involved, on a firm scientific basis. In the Chapter on the exponential theorem and logarithms, I have ventured to introduce the term "generalized logarithm" for the doubly infinite series of values of the logarithm of a quantity.”

E. W. Hobson (1856–1933) British mathematician

A Treatise on Plane Trigonometry https://books.google.com/books?id=_ktLAAAAMAAJ (1891) Preface

Books, Parting

“In the application of the ordinary principles of geometry and trigonometry to such Astronomical measures… it may sometimes be expedient to resolve the process into several successive steps, and these steps may perhaps require different kinds of treatment. But… all are simple and within ordinary comprehension, and the only complexity arises from the circumstance that the student may find it necessary to have a clear view of several such steps at once…”

George Biddell Airy (1801–1892) English mathematician and astronomer

Introduction
Popular Astronomy: A Series of Lectures Delivered at Ipswich (1868)

Success

“And last of all we have the secondary forms of crystals bursting in upon us, and sparkling in the rigidity of mathematical necessity and telling us, neither of harmony of design, usefulness or moral significance, — nothing but spherical trigonometry and Napier's analogies. It is because we have blindly excluded the lessons of these angular bodies from the domain of human knowledge that we are still in doubt about the great doctrine that the only laws of matter are those which our minds must fabricate, and the only laws of mind are fabricated for it by matter.”

James Clerk Maxwell (1831–1879) Scottish physicist

Essay "Analogies in Nature" (February 1856), reprinted in The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862 edited by P.M. Harman, p. 376 (the quote appears on p. 383 http://books.google.com/books?id=zfM8AAAAIAAJ&lpg=PP1&pg=PA383#v=onepage&q&f=false)

Law, Mathematics, Knowledge

“The absolute requisites for the study of this work… are a knowledge of algebra to the binomial at least, plane and solid geometry, plane trigonometry, and the most simple part of the usual applications of algebra to geometry.
…A. De Morgan. London July 1, 1836”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

The Differential and Integral Calculus (1836)

Knowledge, Study, Parting