| While the very formidable Carl Friedrich
Gauss had explored the binomial theorem as a teenager and made a
name for himself
|
| in the international astronomical
community by his accurate predictions of the orbit of the
newly-observed asteroid Ceres, there are |
| other indications that Arthur Conan Doyle
might have had someone else in mind. A possible
candidate is Simon Newcomb (1835-1909) |
| The Binomial Theorem has a long history
going back to Euclid in the 4th century BC and Pingala in India
in the 3rd century BC. |
|
In the 10th century Indian mathematician Halayudha wrote a
commentary on Pingala and the 10th century Persian mathematician |
| Abu Bakr ibn Muhammad ibn al Husayn
al-Karaji also wrote at length on what became known as Pascal's
Triangle. From China there |
| was similar work by Yang Hui (1238-1298)
as well as his predecessor Jia Xian (1010-1070). Blaise Pascal
(1623-1662), despite poor |
|
health for many years, managed to collect and extend many
results in 1658, but it was Newton's work in the 1660s that
really made the |
|
binomial theorem a powerful tool. Newcomb's own work on the
Binomial Theorem was not notable, although he did make a great
many |
|
contributions to astronomy. Of interest in the context of BEISA
is the use of older French observations of planetary positions
by |
|
Newcomb to correct marine navigation tables (based
on smaller samples and fewer years). It is not obvious why Doyle
chose the |
|
Binomial Theorem or asteroid orbital calculations as high water
marks for Moriarty. |
|
With considerable regret, we must go further back in time to
1810. Alas, not to watch the Feanorian mind of Gauss at work,
but rather |
|
to confront a mystery worthy of Sherlock Holmes. |
|
© 2018 Peter F. Zoll. All rights reserved. |