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History Of Mathematics Quotes

Browse 26 quotes about History Of Mathematics.

History Of Mathematics Quotes

“Russell’s paradox threatened to deal a far more serious blow to set theory than earlier ideological objections. The problem was this: consider a set of objects – all possible types of cheesecake, say. This set may include any number of different cheesecakes (New York cheesecake, German Käsekuchen, lemon ricotta, etc.) but, because a set is not literally a cheesecake, the set of all cheesecakes is not a member of itself. The set of all things that are not cheesecakes, on the other hand, is a member of itself. But what, Russell wondered, about the set of all sets that are not members of themselves. If this is not a member of itself, then, by definition, it should be (because its members do not include itself). Conversely, if it is a member of itself, then it should not be (because it does). This was Russell’s paradox in a nutshell. His analysis of the paradox revealed it to be similar in form to several others, including the liar’s paradox (‘this statement is a lie’). ‘It seemed unworthy of a grown man to spend time on such trivialities,’ he complained, desperate for a solution, ‘but what was I to do?”

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Book:The Man from the Future: The Visionary Ideas of John von Neumann
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“While twentieth-century physicists were not able to identify any convincing mathematical constants underlying the fine structure, partly because such thinking has normally not been encouraged, a revolutionary suggestion was recently made by the Czech physicist Raji Heyrovska, who deduced that the fine structure constant, ...really is defined by the [golden] ratio ....”

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Book:The Purposeful Universe: How Quantum Theory and Mayan Cosmology Explain the Origin and Evolution of Life
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“The golden ratio, as well as the Great Pyramid as an expression of it, is an important key to our universe containing the Earth and the Moon. ... The ratio between the Earth and the Moon is in fact the basis for the mathematical concept of 'squaring the circle' ...”

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Book:The Great Pyramid of Giza: A Modern View on Ancient Knowledge
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“Thousands of years ago the ancients had an advanced mathematical understanding of universe that is revealed in many sources. There is a consistent link to knowledge of the golden mean, but the way in which the ancients were able to formulate and use this information speaks of a technical grasp of the subject that exceeds what we know about it in the present day.”

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Book:The Lamb Slain With A Golden Cut: Spiritual Enlightenment and the Golden Mean Revelation
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“Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind. Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ... To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples.”

NumbersPhysicsCosmosHistory Of ScienceFine Structure ConstantPiGolden RatioHistory Of MathematicsConstants Of NatureAncient EgyptiansPythagorasGolden ProportionPhiFibonacci
Author:Jonathan Black, Mark Booth
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“In short, the idea dawns that the one universal principle which possibly ... between force and structure, the embodiment of the Principle of Least Action and the (unknown) force, which in mathematics is known as the attractor which pulls ... in the direction of the most optimal and relatively stable self-organized criticality, could very well be the Golden Ratio dynamic. the universal principle which as the balance between finiteness and infinity, stability and flexibility underlies self-similar fractal forms emerging at the 'edge of chaos' indeed seems to be the Golden Ratio Spiral.”

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Book:Whole Elephant Revealed: Insights into the Existence and Operation of Universal Laws and the Golden Ratio
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“The Great Pyramid was a fractal resonator for the entire Earth. It is designed according to the proportions of the cosmic temple, the natural pattern that blends the two fundamental principles of creation. The pyramid has golden ratio, pi, the base of natural logarithms, the precise length of the year and the dimensions of the Earth built into its geometry. It demonstrates.... As John Michell has pointed out in his wonderful little book, City of Revelation, 'Above all, the Great Pyramid is a monument to the art of 'squaring the circle''.”

History Of MathematicsSacred GeometryGreat PyramidSquaring The CircleJohn Michell
Book:The Lamb Slain With A Golden Cut: Spiritual Enlightenment and the Golden Mean Revelation
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“The conclusion that the Egyptians of the Old Kingdom were acquainted with both the Fibonacci series and the Golden Section, says Stecchini, is so startling in relation to current assumptions about the level of Egyptian mathematics that it could hardly have been accepted on the basis of Herodotus' statement alone, or on the fact that the phi [golden] proportion happens to be incorporated in the Great Pyramid. But the many measurements made by Professor Jean Philippe Lauer, says Stecchini, definitely prove the occurrence of the Golden Section throughout the architecture of the Old Kingdom.... Schwaller de Lubicz also found graphic evidence that the pharonic Egyptians had worked out a direct relation between pi and phi in that pi = phi^2 x 6/5.”

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Book:Secrets of the Great Pyramid: Two Thousand Years of Adventures & Discoveries Surrounding the Mysteries of the Great Pyramid of Cheops
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“Petrie found nothing that disproved the pyramidologist's assumption that the Great Pyramid had been built according to a master plan. Indeed, he describes the Pyramid's architecture as being filled with extraordinary mathematical harmonies and concordances: those same strange symmetries that had so haunted the pyramidologist. Petrie not only noted, for example, that the proportions of the reconstructed pyramid approximated to pi - which others have since elaborated to include those twin delights of Renaissance and pyramidological mathematicians, the Golden Section and the Fibonacci Series ...”

Golden RatioHistory Of MathematicsGreat PyramidFibonacci Sequence
Book:The Great Pyramid: Ancient Egypt Revisited
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“In his ... 'Geometrical peculiarities of the Pyramids', Ballard shows the relationship between the equal area theory and the golden number. After checking Herodotus' statement via dimensions Ballard concludes: 'I have therefore the authority of Herodotus to support the theory which I shall subsequently set forth, that this pyramid was the exponent of lines divided in mean and extreme ratio.”

GeometryGolden RatioHistory Of MathematicsGreat PyramidAncient Egyptians
Book:The Shape of the Great Pyramid
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“...men are capable of perceiving the Pyramid in an astonishing number of ways. Some have thought the Pyramid was an astronomic and astrological observatory. Some have thought it functioned as the equivalent of a theodolite for surveyors in ancient times... Some think it performed as a giant sundial... Some think it records the mathematics and science of a civilization which vanished... Some think it is a huge water pump. Others have thought it was filled with fabulous treasures... One early investigator came away convinced it was the remains of a huge volcano. Another thought the pyramids were Joseph's granaries. Some thought they were heathen idols which should be destroyed. Some believe the Pyramid captures powerful cosmic energies... Some think it is a tomb. Some think it is a Bible in stone with prophecies built into the scheme of its internal passages... Some think it was a mammoth public works project which consolidated the position of the pharaoh and the unity of the nation. Some think it was built by beings from outer space. Some say it was a temple of initiation. Some hold that it was an instrument of science. Some believe it is an altar of Guild built through direct Divine Revelation. And today, judging by the uses to which it has been put, some apparently think it is an outhouse.”

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Book:Pyramid Odyssey
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“The Golden Ratio defines the squaring of a circle. Stated in mathematical terms, this says: Given a square of known perimeter, create a circle of equal circumference. According to some, in ancient Egypt, this mathematical mystery was encoded in the measurements of the Great Pyramid of Giza.”

MathematicsGeometryAncient EgyptGolden RatioHistory Of MathematicsSacred GeometrySquaring The Circle
Book:Whole Elephant Revealed: Insights into the Existence and Operation of Universal Laws and the Golden Ratio
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“In the pentagram, the Pythagoreans found all proportions well-known in antiquity: arithmetic, geometric, harmonic, and also the well-known golden proportion, or the golden ratio. ... Probably owing to the perfect form and the wealth of mathematical forms, the pentagram was chosen by the Pythagoreans as their secret symbol and a symbol of health. - Alexander Voloshinov [As quoted in Stakhov]”

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Book:MATHEMATICS OF HARMONY: FROM EUCLID TO CONTEMPORARY MATHEMATICS AND COMPUTER SCIENCE
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“The Pythagoreans... were fascinated by certain specific ratios, ...The Greeks knew these as the 'golden' proportion and the 'perfect' proportion respectively. They may well have been learned from the Babylonians by Pythagoras himself after having been taken prisoner in Egypt. Ratios lay at the heart of the Pythagorean theory of music.”

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Book:Numbers: Their History and Meaning
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“We therefore find that the triangles and rectangles herein described, enclose a large majority of the temples and cathedrals of the Greek and Gothic masters, for we have seen that the rectangle of the Egyptian triangle is a perfect generative medium, its ratio of five in width to eight in length 'encouraging impressions of contrast between horizontal and vertical lines' or spaces; and the same practically may be said of the Pythagorean triangle”

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Book:Harmonic Proportion and Form in Nature, Art and Architecture
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“Schwaller de Lubicz identifies the Golden Mean as "the fundamental scission," or division of one into two, that creates three things - the original whole and two parts, one in golden proportion to the whole and the other in golden proportion to that.”

Golden RatioGolden MeanHistory Of MathematicsAncient EgyptiansGolden Proportion
Book:Matrix of Creation: Sacred Geometry in the Realm of the Planets
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