The English mathematician Brook Taylor (1685-1731) introduced the calculus of finite differences in his Methodus Incrementorum Directa et Inversa, published in 1715. This work contained the famous formula known today as Taylor's formula. In 1772, Lagrange described it as ``the main foundation of differential calculus'' (Wikipedia: Brook Taylor). Taylor also wrote a treatise on … Continue reading Taylor Expansions from India
Month: November 2016
Marvellous Merchiston’s Logarithms
Log tables, invaluable in science, industry and commerce for 350 years, have been consigned to the scrap heap. But logarithms remain at the core of science, as a wide range of physical phenomena follow logarithmic laws [TM103 or search for “thatsmaths” at irishtimes.com]. The method of logarithms was first devised by John Napier, 8th Laird … Continue reading Marvellous Merchiston’s Logarithms
Which is larger, e^pi or pi^e?
Which is greater, $latex {x^y}&fg=000000$ or $latex {y^x}&fg=000000$? Of course, it depends on the values of x and y. We might consider a particular case: Is $latex {e^\pi > \pi^e}&fg=000000$ or $latex {\pi^e > e^\pi}&fg=000000$? We assume that $latex {x}&fg=000000$ and $latex {y}&fg=000000$ are positive real numbers, and plot the function $latex \displaystyle z(x,y) = … Continue reading Which is larger, e^pi or pi^e?
A New Window on the World
The motto of the Pythagoreans was “All is Number” and Pythagoras may have been the first person to imagine that the workings of the world might be understood in mathematical terms. This idea has now brought us to the point where, at a fundamental level, mathematics is the primary means of describing the physical world. … Continue reading A New Window on the World
ThatsMaths 