A crucial link between mathematics and music is nicely illustrated by the Tonnetz, a geometric diagram representing the harmonic relationships between the notes of the musical scale. An early version of the Tonnetz appeared in Leonhard Euler’s book Tentamen novae theoriae musicae (A new theory of music), published in 1739 [TM274 or search for “thatsmaths” at irishtimes.com]. A modern … Continue reading Music and Maths are Inextricably Intertwined.
Tag: Pythagoras
The Waffle Cone and a new Proof of Pythagoras’ Theorem
Jackson an' Johnson / Murphy an' Bronson / One by one dey come / An' one by one to dreamland dey go. [From Carmen Jones. Lyrics: Oscar Hammerstein] Two young high-school students from New Orleans, Ne’Kiya Jackson and Calcea Johnson, recently presented a new proof of the Pythagorean theorem at a meeting of the American … Continue reading The Waffle Cone and a new Proof of Pythagoras’ Theorem
Geodesics on the Spheroidal Earth-II
Geodesy is the study of the shape and size of the Earth, and of variations in its gravitational field. The Earth was originally believed to be flat, but many clues, such as the manner in which ships appear and disappear at the horizon, and the changed perspective from an elevated vantage point, as well as … Continue reading Geodesics on the Spheroidal Earth-II
Geodesics on the Spheroidal Earth – I
Both Quito in Ecuador and Singapore are on the Equator. One can fly due eastward from Singapore and reach Quito in due course. However, this is not the shortest route. The equatorial trans-Pacific route from Singapore to Quito is not a geodesic on Earth! Why not? The General Equation for Geodesics Open a typical text … Continue reading Geodesics on the Spheroidal Earth – I
The Tunnel of Eupalinos in Samos
The tunnel of Eupalinos on the Greek island of Samos, over one kilometre in length, is one of the greatest engineering achievements of the ancient world [TM098, or search for “thatsmaths” at irishtimes.com]. Approximate course of the tunnel of Eupalinos in Samos. Modern Tunnels The Gotthard Base Tunnel opened in June and will be fully … Continue reading The Tunnel of Eupalinos in Samos
The Biggest Harp in Ireland
This week’s That’s Maths column in The Irish Times (TM052, or search for “thatsmaths” at irishtimes.com) is about "Samuel Beckett Playing Bridge in Dublin". Mathematics Models Nature The life of Pythagoras is shrouded in myth and legend. He was born on the island of Samos and travelled to Egypt, Mesopotamia and possibly India before arriving … Continue reading The Biggest Harp in Ireland
Temperamental Tuning
Every pure musical tone has a frequency, the number of oscillations per second in the sound wave. Doubling the frequency corresponds to moving up one octave. A musical note consists of a base frequency or pitch, called the fundamental together with a series of harmonics, or oscillations whose frequencies are whole-number multiples of the fundamental … Continue reading Temperamental Tuning
The School of Athens
That's Maths in the Irish Times this week ( TM024: search for "thatsmaths" ) deals with perspective in art and its mathematical expression as projective geometry. The study of geometry evolved from measuring plots of land accurately and from the work of builders and carpenters. So Euclidean geometry emerged from the needs of artisans. Another … Continue reading The School of Athens
Pythagoras goes Global
Spherical trigonometry has all the qualities we expect of the best mathematics: it is beautiful, useful and fun. It played an enormously important role in science for thousands of years. It was crucial for astronomy, and essential for global navigation. Yet, it has fallen out of fashion, and is almost completely ignored in modern education. … Continue reading Pythagoras goes Global
ThatsMaths 