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Resonance

January 2004
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Blaise Pascal

Blaise Pascal was born at Clermont on June 19, 1623, and died at Paris on August 19, 1662. Initially, his education was confined only to the study of languages, and did not include any mathematics. As a twelve-year old, having heard from his tutor that geometry was the science of constructing exact figures and of determining the proportions between their different parts, Pascal was stimulated into giving up his play-time to the study of geometry. He discovered by himself that the sum of the angles of a triangle is equal to two right angles. Soon after, he read and quickly mastered Euclid’s Elements. At the age of fourteen he started attending the weekly meetings of French mathematicians like Mersenne, Gassendi, Roberval, Carcavi, Auzout, Mydorge and, Desargues.Pascal wrote an essay on conic sections which was published only much later in 1779.Among these is the famous “Mystic hexagon theorem” asserting that, for any hexagon inscribed in a conic, the points of intersection of the opposite sides are collinear. Pascal’s mystic hexagon is invariant under canonical projection; indeed, along with his friend Desargues, he is a pioneer of projective geometry.It should be noted that the curve known as the ‘limacon of Pascal’ was discovered by the father Etienne Pascal.

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Address for Correspondence

B Sury
Indian Statistical Institute, Bangalore.

The Wright Family

The story of the first powered flight is incomplete without a few words about the remarkable Wright family, for in many ways the Wright Flyer was a family project. First of all the two brothers were both so deeply involved in it that much of the world thinks of them only jointly. Furthermore the project had the blessings of the father, a remarkable bishop and teacher himself; the sum of $ 1000 he gave to Wilbur and Orville was used as a corpus fund by the brothers, who drew on its interest and on their own other resources for their expenditure on the project. Then there was their very intelligent sister Katherine, the only graduate in the family, who not only tended house after the mother passed away (when only 36) but gave intense and warm support to the brothers and kept worrying herself about their progress.

Wilbur and Orville owned their toys jointly. Among the gifts the boys got from their father was a helicopter driven by a rubber band, of a kind still seen but made first by the French engineer Alphonse Penaud (the principle going back to another famous engineer and artist, Leonardo da Vinci). This toy set the boys thinking about flight.

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Address for Correspondence
R Narasimha,
NIAS, Bangalore

Indian Academy of Sciences
C.V.Raman Avenue, Post Box No. 8005,
Sadashivanagar Post, Bangalore 560 080