46 posts on mathematics. All posts · RSS feed
Simple chemical reactions can be balanced by inspection. For example, for the following reaction: since the number of each type of atom must be the same on each side of the reaction, one molecule of ethanol () must produce two molecules of and three of …
An algorithm to find the equation of the circle containing three (non-colinear) points.
A recent tweet by @iwontoffendyou posed the following problem: with reference to the figure below, what is the radius of the orange circle, which is tangent to the $y$-axis, the unit circle and the curve $y = \sqrt{x}$?
The Spiral of Theodorus (also known as the Snail of Pythogoras), illustrated below, is a well-known visualization of the square roots of the integers as the length of the hypotenuses of a sequence of right triangles, placed edge-to-edge. The Spiral of Theodorus [Pbroks13 at English …
A Dyck path can be described as a sequence of horizontal steps for which, at each step a vertical step of or is taken subject to the constraints that the vertical coordinate never decreases below its initial value and the number of "up" and "down" …
Inspired by David Richeson's applet on GeoGebra the Python script below plots the lines joining pairs of points, evenly spaced on the perimeter of a circle according to the following algorithm: label the points ; then join point to point . The line segments inside …
A goat is tethered on the perimeter of a circular paddock of grass by a rope of length . What should be to allow the goat to graze on a maximum of half the area of the paddock? This is a famous problem in recreational …
A Maurer rose is a shape formed by connecting the points on a rose defined in the polar coordinate system by for some positive integer, . The points to join are, in polar coordinates using degrees: For example, the Maurer rose defined by is: The …
The Weierstrass function, named after the German mathematician Karl Weierstrass (1815 – 1897) is a real-valued function that is continuous everywhere but nowhere differentiable. It is usually expressed as a Fourier series: where and is a positive, odd integer satisfying . The code below plots …
A recent article, Narushin et al., "Egg and math: introducing a universal formula for egg shape", Ann. N.Y. Acad. Sci. 1505, 169 (2021) introduces a "universal" formula for the shape of eggs, including "pyriform" (pear-shaped) eggs such as those of the guillemot – supposedly, such …
