Common-or-Garden Ellipses In an earlier post we saw how a gardener may set out oval flower-beds using a well-known property of ellipses: the sum of the distances from any point on the ellipse to the two foci is always the same value, $latex {2a}&fg=000000$, the length of the major axis. The gardener puts down two stakes … Continue reading Drawing Multi-focal Ellipses: The Gardener’s Method
Month: August 2017
Locating the HQ with Multi-focal Ellipses
Motivation Ireland has four provinces, the principal city in each being the provincial capital: Belfast, Cork, Dublin and Galway. The map here shows the location of these cities. Now imagine a company that needs to visit and to deliver goods frequently to all four cities. Where might they locate their HQ to minimize transport costs … Continue reading Locating the HQ with Multi-focal Ellipses
Saros 145/22: The Great American Eclipse
Next Monday, the shadow of the Moon will bring a two-minute spell of darkness as it sweeps across the United States along a path from Oregon to South Carolina. The eclipse is one of a series known as Saros 145. [TM121 or search for “thatsmaths” at irishtimes.com]. Dynamics of Eclipses If the Moon moved in … Continue reading Saros 145/22: The Great American Eclipse
Fractions of Fractions of Fractions
Numbers can be expressed in several different ways. We are familiar with whole numbers, fractions and decimals. But there is a wide range of other forms, and we examine one of them in this article. Every rational number $latex {x}&fg=000000$ can be expanded as a continued fraction: $latex \displaystyle x = a_0 + \cfrac{1}{ a_1 … Continue reading Fractions of Fractions of Fractions
It’s as Easy as Pi
Every circle has the property that the distance around it is just over three times the distance across. This has been known since the earliest times [see TM120 or search for “thatsmaths” at irishtimes.com]. The constant ratio of the circumference to the diameter, denoted by the Greek letter pi, is familiar to every school-child. You … Continue reading It’s as Easy as Pi
