This time I review the book A History of Pi from Petr Beckmann.
It took me some time finishing it, but I really enjoyed most of it.
The book claims to be written neither by a historian, nor a mathematican.
But it covers a lot of historical background and lots of formulars.
- Euclidian approximations,
- Calculus approximations,
- Computer approximations,
The first calculations are based on the contents of Euclid's Elements.
Basically the area of a circle are approximated by a series of polygons, whose area is known.
The results are rational numbers, that achieve an impressing accuracy.
- finite number of steps,
- only ruler and circle.
After Newton and Leibniz π can be approximated to a far better accuracy.
Instead of rationals, the number are represented in decimal notation. Far more digits of π are calculated by human computers.
- infinte number of steps,
- integrals and power series.
The history of computer based calculation stops at 750.000 digits.
- first digit records.
What I liked about the book
Each achievement is set into context. The main actors are introduced. Common prejudgements are contered.
I like historical facts and the author presents them in a pleasant way.
- Vivid Background,
Beside π I learned a lot from this book.
For example the development of counting is supported by the different names of the numbers.
What I didn't like so much
Due to the age of the typesetting, the formulas are hard to read. Square roots lack their upper beam and some bits of symbols and numbers haven't got enough ink.
The book critics a number of times to Siberian Prison Camps in Russia.
In our times, this style of propaganda and political statement in a scientific text seems out of place.
I enjoyed reading the book.
You recognize its age (it was released 1976). But its describes the livelong struggle of mankind to cope with this magic number.