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Basic structure of the Unit-Circle.
Precalculus_Trigonometric_Pythagorean_Identities.
Precalculus_Trigonometric_Double_Angle_Formulas.
Precalculus_Trigonometric_Half_Angle_Identities.
Precalculus_Trigonometric_Sum_and_Difference_Formulas.
Precalculus_Trigonometric_Product_to_Sum_Formulas.
Precalculus_Trigonometric_Power_Reducing_Formulas.
Precalculus_Trigonometric_Sum_to_Product_Formulas.
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It may well be doubted whether, in all the range of science, there is any field so fascinating to the explorer - so rich in hidden treasures - so fruitful in delightful surprises - as Pure Mathematics.  Lewis Carroll
The charm [of mathematics] lies chiefly in the absolute certainty of its results; for that is what, beyond all mental treasures, the human intellect craves for. Let us be sure of something! More light, more light!  Lewis Carroll
Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings.  Alfred North Whitehead
The science of Pure Mathematics, in its modern developments, may claim to be the most original creation of the human spirit.  Alfred North Whitehead
All science as it grown toward perfection becomes mathematical in its ideas.  Alfred North Whitehead
Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of paintings or music, yet sublimely pure and capable of a stern perfection such as only the greatest art can show.  Bertrand Russell
Although this may seem a paradox, all exact science is dominated by the idea of approximation.  Bertrand Russell
Creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.  Eric Temple Bell
'Obvious' is the most dangerous word in mathematics.  Eric Temple Bell
To appreciate the living spirit rather than the dry bones of mathematics, it is necessary to inspect the work of a master at first hand. Textbooks and treatises are an unavoidable evil... The very crudities of the first attack on a significant problem by a master are more illuminating than all the pretty elegance of the standard texts which has been won at the cost of perhaps centuries of finicky polishing.  Eric Temple Bell
I have often admired the mystical way of Pythagoras, and the secret magic of numbers.   Sir Thomas Browne
The structures with which mathematics deals are more like lace, the leaves of trees and the play of the light and shadow on a human face than they are like buildings and machines, the least of their representatives.  Scott Buchanan
Examinations are formidable even to the best prepared, for the greatest fool may ask more than the wisest man can answer.  Charles Caleb Colton
Algebra is generous; she often gives more than is asked of her.   Jean D'Alembert
Mathematics is the supreme arbiter. From its decisions there is no appeal.  Tobias Dantzig
Mathematics seems to endow one with something like a new sense.  Charles Darwin
Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics.  Leonardo da Vinci
Whoever despises the high wisdom of mathematics nourishes himself on delusion.  Leonardo da Vinci
The popular image of mathematics as a collection of precise facts, linked together by well-defined logical paths is revealed to be false. There is randomness and hence uncertainty in mathematics, just as there is in physics.  Paul Davis
One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories.  Philip Davis
The creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.  Albert Einstein
We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact, mathematics is, to a large extent, invention of better notations.  Richard P. Feynman
Mathematicians are like lovers ... Grant a mathematician the least principle, and he will draw from it a consequence which you must grant him also, and from this consequence another.  Bernard de Fontenelle
Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.   David Hilbert
[The] sole end of science is the honor of the human mind, and ... under this title a question about numbers is worth as much as a question about the system of the world.  Carl Jacobi
Where there is matter, there is geometry.  Johannes Kepler
Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.  Felix Klein
The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.  Sir Isaac Newton
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.  George Polya
Geometry is knowledge of the eternally existent.  Pythagoras
In mathematics, if a pattern occurs, we can go on to ask, Why does it occur? What does it signify? And we can find answers to these questions. In fact, for every pattern that appears, a mathematician feels he ought to know why it appears.   W. W. Sawyer
Futile is the labor of those who fatigue themselves with calculations to square the circle. Michael Stifel
The most distinct and beautiful statement of any truth must take at last the mathematical form.  Henry David Thoreau
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality   Albert Einstein
Mathematics is a game played according to certain simple rules with meaningless marks on paper.   David Hilbert
To teach is to learn twice. -- Joseph Joubert
The mediocre teacher tells. The good teacher explains.The superior teacher demonstrates. The great teacher inspires. -- William Arthur Ward
A fool's brain digests philosophy into folly, science into superstition, and art into pedantry. Hence University education. -- George Bernard Shaw
University politics are vicious precisely because the stakes are so small. -- Henry Kissinger
Knowledge comes, but wisdom lingers. -- Alfred, Lord Tennyson
Let us be thankful for the fools. But for them the rest of us could not succeed. -- Mark Twain
When a true genius appears in the world you may know him by this sign: that all the dunces are in confederacy against him. -- Johnathan Swift
Irrationally held truths may be more harmful than reasoned errors. -- Thomas Henry Huxley
An expert is a person who has made all the mistakes that can be made in a very narrow field. -- Niels Bohr
The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. -- Albert Einstein
If we knew what we were doing, it wouldn't be called research, would it? -- Albert Einstein
Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning. -- Rich Cook
Celestial navigation is based on the premise that the Earth is the center of the universe. The premise is wrong, but the navigation works. An incorrect model can be a useful tool. -- Kelvin Throop III
A human being is a part of the whole, called by us Universe, a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest--a kind of optical delusion of his consciousness. This delusion is a kind of prison, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free from this prison by widening our circle of compassion to embrace all living creatures and the whole nature in its beauty. -- Albert Einstein
Whether you think that you can, or that you can't, you are usually right. -- Henry Ford