Quotations (19)

The Golden Ratio

the Story of Phi, the World's Most Astonishing Number
1 to 19 of 19 items
In his book Fads and Fallacies in the Name of Science, Gardner writes: If one looks up the facts about the Washington Monument in the World Almanac, he will find considerable fiveness. Its height is 555 feet and 5 inches. The base is 55…
Arithmetic operations with Roman numerals are not fun. For example, to obtain the sum of 3,786 and 3,843, you would need to add MMMDCCLXXXVI to MMMDCCCXLIII; if you think that is cumbersome, try multiplying those numbers. === For example,…
the Fibonacci sequence; 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,…, and this time let us look at the ratios of successive numbers (calculated here to the sixth decimal place): 1/1 = 1.000000 2/1 = 2.000000 3/2 =…
George Burns (in his book How to Live to Be 100 or More) once put it: “How do you live to be 100 or more? There are certain things you have to do. The most important one is you have to be sure to make it to 99.” === “God created the…
To see a World in a Grain of Sand, And a Heaven in a Wild Flower, Hold Infinity in the Palm of your hand, And Eternity in an hour. === The name “equiangular” reflects another unique property of the logarithmic spiral. If you draw a…
Accepting the general principle of the Copernican heliocentric system, he set out to search for answers to the following two major questions: Why were there precisely six planets? and What was it that determined that the planetary orbits…
Similarly, modern theories known as string theories use basic entities (strings) which are extremely tiny (more than a billion billion times smaller than the atomic nucleus) to deduce the properties of all the elementary particles. Like a…
In an experiment conducted in 1966 by H. R. Schiffman of Rutgers University, subjects were asked to “draw the most aesthetically pleasing rectangle” that they could on a sheet of paper. After completion, they were instructed to orient the…
Goethe expressed elsewhere his opinion on mathematics thus: “The mathematicians are a sort of Frenchmen: when you talk to them, they immediately translate it into their own language, and right away it is something entirely…
Build thee more stately mansions, O my soul, As the swift seasons roll! Leave thy low-vaulted past! Let each new temple, nobler than the last, Shut thee from heaven with a dome more vast, Till thou at length art free, Leaving thine…
Periodic tilings also can be generated with more complex shapes. One of the most astounding monuments of Islamic architecture, the citadel-palace Alhambra in Granada, Spain, contains numerous examples of intricate tilings (Figure 95). Some…
Paul Steinhardt was one of the key figures in the development of what is known as the inflationary model of the universe. According to this model, originally proposed by physicist Alan Guth of MIT, when the universe was only a tiny…
An old mathematical joke tells of a physicist who thought that he could become rich from betting at horse races by solving the exact equations of motion for the horses. After much work, he indeed managed to solve the equations—for…
Fractal diagrams partake Of the essence sensed by Blake. Basic forms will still prevail Independent of the Scale; Viewed from far or viewed from near Special signatures are clear. When you magnify a spot, What you had before, you’ve…
The main innovation in Mandelbrot’s theory, as compared to standard portfolio theory, is in its ability to reproduce tumultuous trading as well as placid markets. Portfolio theory, on the other hand, is able to characterize only relatively…
Some people think one thing is beautiful, some another. Socialist construction is a beautiful thing and stimulates people here. Before the Cultural Revolution some of us believed in the beauty of mathematics but failed to solve practical…
Any sequence of 200 genuine coin tosses contains a run of six consecutive heads or six consecutive tails with a very high probability. On the other hand, people trying to fake a sequence of coin tosses very rarely believe that they should…
Godfrey H. Hardy was always proud of having “never done anything ‘useful.’ ” === An Eternal Golden Braid: “Provability is a weaker notion than truth.” In this sense, there will never be a formal method of determining for every mathematical…
Mathematics thus is, in some sense, the language of the universe—of the universe discerned by humans. === Christopher Marlowe (1564–1593) : Nature that framed us of four elements, Warring within our breasts for regiment, Doth teach us all…