## Archive for September, 2016

### Negative Number Names

The counting numbers that we learn as children are so familiar that using them is second nature. They bear the appropriate name natural numbers. From then on, names of numbers become less and less apposite.

### Venn Again’s Awake

We wrote about the basic properties of Venn diagrams in an earlier post. Now we take a deeper look. John Venn, a logician and philosopher, born in Hull, Yorkshire in 1834, introduced the diagrams in a paper in 1880 and in his book Symbolic Logic, published one year later. The diagrams were used long before Venn’s paper, but he formalized and popularized them. He used them as logical diagrams: the interior of each set means the truth of a particular proposition. Unions and intersections of sets correspond to the logical operators OR and AND.

### The next Hamilton

William Rowan Hamilton was Ireland’s greatest mathematician. His name is heard thousands of times every day throughout the world when researchers use the Hamiltonian function that encapsulates the dynamics of a vast range of physical systems. He achieved fame early in life and remains one of the all-time great scientists. [TM099, or search for “thatsmaths” at irishtimes.com].

### Heron’s Theorem: a Tool for Surveyors

Heron was one of the great Greek mathematicians of Alexandria, following in the tradition of Euclid, Archimedes, Eratosthenes and Apollonius. He lived in the first century, from about AD 10 to AD 70. His interests were in practical rather than theoretical mathematics and he wrote on measurement, mechanics and engineering. He devised a steam-powered device and a wind-wheel that operated an organ. He is regarded as the greatest experimenter of antiquity, but it is for a theorem in pure geometry that mathematicians remember him today.

Heron of Alexandria. Triangle of sides a, b and c and altitude h.

### 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.