In an earlier post, we discussed Grandi's series, originally studied by the Italian monk Dom Guido Grandi around 1703. It is the series $latex \displaystyle G = 1 - 1 + 1 - 1 + 1 - 1 + \dots &fg=000000$ This is a divergent series: the sequence of partial sums is $latex {\{ 1, … Continue reading Grandi’s Series: A Second Look
Month: July 2018
The Empty Set is Nothing to Worry About
Today's article is about nothing: nothing at all, as encapsulated in the number zero and the empty set. It took humanity millennia to move beyond the counting numbers. Zero emerged in several civilizations, first as a place-holder to denote a space or gap between digits, and later as a true number, which could be manipulated … Continue reading The Empty Set is Nothing to Worry About
Grandi’s Series: Divergent but Summable
Is the Light On or Off? Suppose a light is switched on for a half-minute, off for a quarter minute, on for one eighth of a minute and so on until precisely one minute has elapsed. Is the light on or off at the end of this (infinite) process? Representing the two states ``on'' and … Continue reading Grandi’s Series: Divergent but Summable
Trigonometric Comfort Blankets on Hilltops
On a glorious sunny June day we reached the summit of Céidín, south of the Glen of Imall, to find a triangulation station or trig pillar. These concrete pillars are found on many prominent peaks throughout Ireland, and were erected to aid in surveying the country [see TM142, or search for “thatsmaths” at irishtimes.com]. The pillars are about … Continue reading Trigonometric Comfort Blankets on Hilltops
ThatsMaths 