Most people are aware of two or three basic tests for divisibility by a prime number: A number n is divisible by 2 iff it ends in an even number (0, 2, 4, 6, or 8) by 5 iff it ends in a 0 or a 5 by 3 iff its digits add up to a multiple of 3 These…
Month: June 2016
Polygons as Functions
A recent comment from a colleague got me thinking about describing polygons using functions. His intent was that polygons (and all closed shapes) can be described as sets of functions; for instance, a triangle could be described by three linear functions with the domain of the triangle’s vertices. And, of course, any closed shape cannot…
Indefinite vs infinite
I have borrowed from a colleague a copy of G. A. Wentworth’s Plane and Solid Geometry, copyright 1899 and published 1902 by The Athenæum Press of Boston. I enjoy reading old textbooks because they either reinforce or give lie to certain claims about the longevity of mathematical concepts. This particular volume is attractive to me as…
Rationals except Zero
Here’s a quick one: All rational numbers except 0 can be expressed as \[(-1)^s \Pi p_i^{n_i}\] where \(s \in \{0, 1\}\), \(p_i\) is a prime number, and \(n_i\) is an integer. This reminds me of the restriction on the definition of rationals, i.e., that \(\frac{a}{b}\) is a rational number for all integers \(a\) and \(b\)…
Defining a Line
The version of Geometry most widely taught in high schools in the United States is an amalgam of the two most basic fields of geometry: Synthetic and analytic. The mixing of these two is done in such a way as to suggest that the fields are complementary, and so the points of differentiation between the…
claustrophobia
i am overwhelmed by the wall by the river by the stream of gogogodododostopstopstopnownownow until i am left breathless suffocated by another day of doing nothing — ptkh 06.11.16
But is it math?
It is a persistently popular thing to do on social media to post challenges like this one. I used to be of a mind to be outraged at the abuse of the equal sign: Clearly these are not addition problems! This is not how math symbolism works! This is not math! However, I’ve since shifted…