By Paul J. Nahin

What's the top option to picture a rushing bullet? Why does mild go through glass in the slightest degree period of time attainable? How can misplaced hikers locate their means out of a wooded area? what's going to rainbows appear like sooner or later? Why do cleaning soap bubbles have a form that provides them the least quarter? by means of combining the mathematical historical past of extrema with modern examples, Paul J. Nahin solutions those interesting questions and extra during this attractive and witty quantity. He exhibits how lifestyles frequently works on the extremes--with values turning into as small (or as huge) as possible--and how mathematicians over the centuries have struggled to calculate those difficulties of minima and maxima. From medieval writings to the advance of contemporary calculus to the present box of optimization, Nahin tells the tale of Dido's challenge, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and extra. alongside the way in which, he explores the best way to construct the shortest bridge attainable among cities, tips on how to store for rubbish luggage, tips on how to differ velocity in the course of a race, and the way to make the best basketball shot. Written in a conversational tone and requiring basically an early undergraduate point of mathematical wisdom, whilst Least is better is stuffed with attention-grabbing examples and ready-to-try-at-home experiments. this can be the 1st publication on optimization written for a large viewers, and math fanatics of all backgrounds will relish its energetic subject matters

Show description

Read or Download When least is best : how mathematicians discovered many clever ways to make things as small (or as large) as possible PDF

Similar mathematics books

Meeting the Needs of Your Most Able Pupils in Maths (The Gifted and Talented Series)

Assembly the wishes of Your so much capable students: arithmetic presents particular assistance on: recognising excessive skill and power making plans, differentiation, extension and enrichment in Mathematicss instructor wondering talents help for extra capable scholars with special academic needs (dyslexia, ADHD, sensory impairment) homework recording and review past the school room: visits, competitions, summer season colleges, masterclasses, hyperlinks with universities, companies and different organizations.

Additional info for When least is best : how mathematicians discovered many clever ways to make things as small (or as large) as possible

Sample text

It also promises that codes exist that approach the theoretical bounds when the code dimension and delay become large. An important theorem in this branch is the source coding theorem [17]: Source coding theorem: There exists a mapping from source symbols to codewords such that for a given distortion D, R(D) bits=symbol are su cient to achieve an average distortion that is arbitrarily close to D. The function R(D) is known as the rate-distortion function. 4. This function is normally computed using numerical methods [18], although for simple source and distortion models it can be computed analytically.

13: A vector quantization system ÿrst decomposed into k-dimensional input vectors. Those input vectors can be generated in a number of di erent ways; they can refer to the pel values themselves or to some appropriate transformation of them. For example, a k = M × M block of pels can be ordered to form a k-dimensional input vector s = [s1 ; : : : ; sk ]T . In VQ, the k-dimensional space R k is divided into N regions, or cells, Ri . Any input vector that falls into cell Ri is represented by a representative codevector ri = [r1 ; : : : ; rk ]T .

This representation serves two purposes. First, luminance ensures backward compatibility with monochrome video. Second, this representation lends itself more easily to video compression. This can be explained as follows. The human visual system (HVS) has poor response to color (chrominance) spatial detail compared to its response to luminance spatial detail [9]. Thus, the chrominance signals can be bandlimited or subsampled to achieve compression. There are three main analog color coding systems: Phase Alternation Line (PAL), SEquential Couleur Avec Memoire (SECAM) and National Television System Committee (NTSC).

Download PDF sample

Rated 4.62 of 5 – based on 28 votes