Bridges to Infinity: The Human side of Mathematics by Guillen

By Guillen

Explains vital mathematical ideas, corresponding to likelihood and statistics, set thought, paradoxes, symmetries, dimensions, online game concept, randomness, and irrational numbers

Show description

Read or Download Bridges to Infinity: The Human side of Mathematics PDF

Best science & mathematics books

Semi-Inner Products and Applications

Semi-inner items, that may be clearly outlined typically Banach areas over the genuine or advanced quantity box, play an incredible position in describing the geometric homes of those areas. This new booklet dedicates 17 chapters to the examine of semi-inner items and its functions. The bibliography on the finish of every bankruptcy includes a checklist of the papers mentioned within the bankruptcy.

Plane Elastic Systems

In an epoch-making paper entitled "On an approximate answer for the bending of a beam of oblong cross-section lower than any method of load with particular connection with issues of targeted or discontinuous loading", acquired through the Royal Society on June 12, 1902, L. N. G. FlLON brought the suggestion of what used to be accordingly referred to as through LovE "general­ ized airplane stress".

Discrete Hilbert-Type Inequalities

In 1908, H. Wely released the well-known Hilbert’s inequality. In 1925, G. H. Hardy gave an extension of it via introducing one pair of conjugate exponents. The Hilbert-type inequalities are a extra large classification of study inequalities that are together with Hardy-Hilbert’s inequality because the specific case.

Extra resources for Bridges to Infinity: The Human side of Mathematics

Example text

For example, one of these constants, the speed of light, has been measured out to nine decimal places, and the digits have yet to show any pattern. 29979245 8 . ) Another constant is one that is descriptive of dynamic behavior at the atomic level. It is called the fine-structure constant, and there is no pattern to its digits even when measured out to ten decimal places. 0072 9 73 5 0 3 . ) In physics alone there are more than a dozen of these constants, which have been measured out to anywhere from a few to eleven decimal places, and not one of them has a pattern to its digits.

The spacing between ticks in a rational number line would correspond to the spacing between images when the two mirrors were infinitely close together-touch­ ing, in other words. The spacing between ticks in a real num­ ber line, however, would correspond to the spacing between the images when the two mirrors were closer than touching. But this could only happen if the mirrors actually entered one another, as Alice entered the looking glass. For scientists interested in learning about time, the im­ ponderability of the real number line poses an interesting choice.

If I were to interchange j ust one pair of digits in its infinitely long random string of digits, I would no longer have the same irrational number. Each irrational number has its unique ran­ domness and each of its digits has a unique role in creating that individualized randomness. 05 7 1 42 8 5 7 1 42 8 5 7 1 4 . . , 1/9 9 i s . 0 1 0 1 0 1 0 1 0 1 . . 0000000 . . ) . Certainly there are many temporal phenomena known to us today that are perfectly describable in terms of rational numbers alone.

Download PDF sample

Rated 4.61 of 5 – based on 32 votes