## Posts Tagged '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]

Euclid’s Theorem I-47, also known as Pythagoras’ Theorem, in Oliver Byrne’s colourful text, The Elements of Euclid.

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 Mathematical Society in Georgia. It has been widely believed that no proof based on trigonometry was possible but we now know that to be false. 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 astronomical phenomena, convinced savants of its spherical shape. In the third century BC, Eratosthenes accurately estimated the circumference of the Earth [TM137 or search for “thatsmaths” at irishtimes.com].

Geodesic at bearing of 60 degrees from Singapore. Passes close to Quito, Ecuador. Note that it is not a closed curve: it does not return to Singapore.

### 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?

A drastically flattened spheroid. Clearly, the equatorial route between the blue and red points is not the shortest path.

### 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.

### 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”.

Image from Tiger Dublin Fringe Festival website.
Photo Credit: Ciara Corrigan

### 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 frequency.

### 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.

### 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.