A History of Pi

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Tom Palven
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A History of Pi

Post by Tom Palven » Tue Jul 31, 2018 1:36 pm

A History of Pi by Petr Beckmann, 1971

Petr Beckmann was born in Czechoslovakia in 1924 and worked as a research scientist for the Czech Academy of Science until 1963 when he became a professor of electrical engineering at the University of Colorado.

From the Preface:
The history of pi is a quaint little mirror of the history of man. It is the story people like Archimedes of Syracuse, whose method of calculating pi defied substantial improvement for some 1900 years; and it is also the story of a Cleveland businessman who published a book in 1931 announcing the grand discovery that pi was exactly equal to 256/81, a value that the Egyptians had used some 4,000 years ago. It is the story of human achievement at the University of Alexandria in the 3rd century B.C.; and it is also the story of human folly which made mediaeval bishops and crusaders burn scientific libraries because they condemned their contents as the works of the Devil.
Being neither an historian nor a mathematician, I felt eminently qualified to write this story.
That remark is meant to be sarcastic, but there is a kernel of truth in it. Not being a historian, I am not obliged to wear the mask of dispassionate aloofness…
Not being a mathematician, I am not obliged to complicate my explanations with excessive mathematical rigor…

CONTENTS
1. Dawn
2. The Belt
3. The Early Greeks
4. Euclid
5. The Roman Pest
6. Archimedes of Syracuse
7. Dusk
8. Night
9. Awakening
10. The Digit Hunters
11. The Last Archimedeans
12. Prelude to Breakthrough
13. Newton
14. Euler
15. The Monte Carlo Method
16. The Transcendence of Pi
17. The Modern Circle Squarers
18. The Computer Age

From chapter 8. NIGHT:

The Middle Ages are usually considered to have ended with the fall of Constantinople in 1453 or the discovery of the New World in 1492, but the insane persecution of science continued well beyond that time…For more than a century longer the Church tolerated no deviation from the literal word of the Bible or the teachings of Aristotle…In 1633, the 70-year old Galileo Galilei went through the torture chambers of the Inquisition until he was willing to sign that “I held that the Earth is not the center of the universe…and I swear that I will never more in the future say or assert anything verbally or in writing that will ever give rise to a similar suspicion of (heresy).”
Thereupon he was sentenced to life imprisonment…in 1642(which was commuted to house arrest).

…250 years later Sir Oliver Lodge commented:
“Poor schemers! Before the year was out an infant was born in Lincolnshire whose destiny it was to round and complete and carry forward the work of their victim, so that until man shall cease from this planet neither Galileo nor his work shall have need of a monument.”

From chapter 13 NEWTON (Dec. 25, 1642-March 31, 1727):

There had never been a scientist like Newton and there has not been one like him since. Not Einstein, not Archimedes, not Galileo, not Planck, not anybody else measured up to anywhere near his stature. Indeed, it is safe to say that there can never be a scientist like Newton again, for the scientists of future generations will have books and libraries, microfilms and microfiches, magnetic discs and other computerized information to draw on. Newton had nothing but except Galileo’s qualitative thoughts and Kepler’s laws of planetary motion. With little more than that to go on, Newton formulated three laws that govern all motion in the universe. From the galaxies in the heavens to the electrons whirling round atomic nuclei, from the cat that always falls on its feet to the gyroscopes that watch over the flight of spaceships. His laws of motion have withstood the test for time for three centuries. The very concept of space, time, and mass have crumbled under the impact of Einstein’s theory of relativity; age-old prejudices of cause, effect and certainty were destroyed by quantum mechanics; but Newton’s laws have come through unscathed.
Last edited by Tom Palven on Tue Jul 31, 2018 2:56 pm, edited 1 time in total.
If one can be taught to believe absurdities, one can commit atrocities. --Voltaire

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landrew
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Re: A History of Pi

Post by landrew » Tue Jul 31, 2018 2:00 pm

It's frequently said that the pyramid builders must have known the value of pi, even though there's no written evidence anywhere. The value of pi can be extracted from the measurements of the Great pyramid at Ghiza. If one divides the perimeter of the Pyramid by its height, one obtains a close approximation to pi.

That proves they knew about pi, right? Not really. Now open your minds a little. Here's how they could have done it without ever having heard of pi: Let's say the builders had a unit of measure; we'll call a "cubit." Their measuring sticks and cords would have been in cubits. But what about a measuring wheel? They may have had a measuring wheel with a 1 cubit diameter, which when rolled along, and compared to a linear cubit measure, the value of pi could be extracted from it. If both tools were used to lay out the design of the pyramid, the value of pi would be contained within.

We're not good at recognizing our own limitations. "It's hard to see what you can't see," therefore we can get stuck behind paradigms for centuries without ever seeing past them. People with imagination and creativity are in short supply. Most of us prefer to live under a set of certitudes without ever questioning them.
The job of a skeptic is to investigate the unexplained; not to explain the uninvestigated.

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Austin Harper
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Re: A History of Pi

Post by Austin Harper » Tue Jul 31, 2018 6:16 pm

You're right. Just because the ratio of those values happens to be approximately equal to another value it doesn't mean that it was intended to be that way. I'm sure if I measured a bunch of lengths of objects on my desk I could also find some ratio that was approximately pi.
Dum ratio nos ducet, valebimus et multa bene geremus.

Matthew Ellard
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Re: A History of Pi

Post by Matthew Ellard » Wed Aug 01, 2018 1:07 am

Austin Harper wrote:You're right. Just because the ratio of those values happens to be approximately equal to another value it doesn't mean that it was intended to be that way. I'm sure if I measured a bunch of lengths of objects on my desk I could also find some ratio that was approximately pi.

This is the whole basis for Salomed "Magic ratios in Shakespeare's Sonnets" claim.

Salomed claimed he could find 5 important mathematical constants, by dividing the distances between certain letters on the front page of the sonnets. When we pointed out to him there were over 16,000,000 other combinations on the same page, he simply removed all the other letters from the image........and made exactly the same claim again in a new thread.
:lol: :lol: :lol:
viewtopic.php?f=80&t=27941&hilit=sonnets#p566177