Ceres (bottom left), the Moon and Earth, shown to scale [Image NASA].
Archive for June, 2021
From a hilltop, the horizon lies below the horizontal level at an angle called the “dip”. Around AD 1020, the brilliant Persian scholar al-Biruni used a measurement of the dip, from a mountain of known height, to get an accurate estimate of the size of the Earth. It is claimed that his estimate was within 1% of the true value but, since he was not aware of atmospheric refraction and made no allowance for it, this high precision must have been fortuitous [TM213 or search for “thatsmaths” at irishtimes.com].
Snowdonia photographed from the Ben of Howth, 12 January 2021. Photo: Niall O’Carroll (Instagram).
Al Biruni and the Size of the Earth
Published June 10, 2021 Occasional ClosedTags: Geometry, History, Trigonometry
Abu Rayhan al-Biruni (AD 973–1048)
Al Biruni at Persian Scholars Pavilion in Vienna.
The 11th century Persian mathematician Abu Rayhan al-Biruni used simple trigonometric results to estimate the radius and circumference of the Earth. His estimate has been quoted as 6,340 km, which is within 1% of the mean radius of 6,371 km. While al-Biruni’s method was brilliant and, for its era, spectacular, the accuracy claimed must be regarded with suspicion.
Al-Biruni assumed that the Earth is a perfect sphere of (unknown) radius 
The Simple Arithmetic Triangle is full of Surprises
Published June 3, 2021 Irish Times ClosedTags: Arithmetic, Number Theory
Pascal’s triangle is one of the most famous of all mathematical diagrams, simple to construct and yet rich in mathematical patterns. These can be found by a web search, but their discovery by study of the diagram is vastly more satisfying, and there is always a chance of finding something never seen before [TM212 or search for “thatsmaths” at irishtimes.com].
Pascal’s triangle as found in Zhu Shiji’s treatise The Precious Mirror of the Four Elements (1303).
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