As someone with an MS and BS in mathematics I was intrigued by this story. I read the links and could not discern precisely what Mr. Gidiney claimed to have discovered. If, as reported in the newspaper, "Mr. Gidney claims that by an algebraic calculation he has discovered the exact ratio" then he was mistaken. (The newspaper might have misquoted him on this technical topic.)
Pi is famously an irrational number. That means it cannot be expressed precisely as the ratio of two integers.
Pi is even more famously a transcendental number. That means it is "not the solution of any non-constant polynomial equation with rational coefficients."
So I would like to see Mr. Gideney's "algebraic proof" to better understand its claim.
The article that Amy referenced by Christine Cooper Rompato describes a bit more of his method: “works by a series of algebraic equations numbering 1350, from which he develops the ratio, 3.135135+.” It’s very possible that the word ratio was chosen by a journalist, not a mathematician.
More info about Gidiney can be found at https://en.everybodywiki.com/Charles_T._Gidiney, where it’s mentioned that “in 1843, Gidiney published a formula to extract the fourth root under “A Concise Formula to Extract the Fourth Root: Example” in The New York State Mechanic, a Journal of the Manual Arts, Trades, and Manufactures.” An excerpt of his thinking on the formula appears in the link.
We're all short many details. But since the first six digits of the approximation of pi are 3.14159 it's likely that Mr. Gidiney's method is incorrect.
Finding the fourth root of something is very different from finding pi (since pi is a transcendental number, it is not the solution to a polynomial equation). So I suspect the formula is unrelated to pi.
Sorry, I didn’t mean they were related but I could have been clearer. More, it showed he had a great deal of interest in mathematics, though the details are sketchy on how he gained an interest in these things.
What a great story. Thanks, Amy, for writing it, and thanks, Andrew, for sharing it.
Very glad to write this up, and to have Andrew run it!
https://en.wikipedia.org/wiki/Pi
As someone with an MS and BS in mathematics I was intrigued by this story. I read the links and could not discern precisely what Mr. Gidiney claimed to have discovered. If, as reported in the newspaper, "Mr. Gidney claims that by an algebraic calculation he has discovered the exact ratio" then he was mistaken. (The newspaper might have misquoted him on this technical topic.)
Pi is famously an irrational number. That means it cannot be expressed precisely as the ratio of two integers.
Pi is even more famously a transcendental number. That means it is "not the solution of any non-constant polynomial equation with rational coefficients."
So I would like to see Mr. Gideney's "algebraic proof" to better understand its claim.
Yes, I'd love to see anything that he wrote about pi. Unfortunately, the only paper trail he left is the letter to the mayor during the Draft Riots.
The article that Amy referenced by Christine Cooper Rompato describes a bit more of his method: “works by a series of algebraic equations numbering 1350, from which he develops the ratio, 3.135135+.” It’s very possible that the word ratio was chosen by a journalist, not a mathematician.
More info about Gidiney can be found at https://en.everybodywiki.com/Charles_T._Gidiney, where it’s mentioned that “in 1843, Gidiney published a formula to extract the fourth root under “A Concise Formula to Extract the Fourth Root: Example” in The New York State Mechanic, a Journal of the Manual Arts, Trades, and Manufactures.” An excerpt of his thinking on the formula appears in the link.
We're all short many details. But since the first six digits of the approximation of pi are 3.14159 it's likely that Mr. Gidiney's method is incorrect.
Finding the fourth root of something is very different from finding pi (since pi is a transcendental number, it is not the solution to a polynomial equation). So I suspect the formula is unrelated to pi.
Sorry, I didn’t mean they were related but I could have been clearer. More, it showed he had a great deal of interest in mathematics, though the details are sketchy on how he gained an interest in these things.
Thank you Amy and Andrew! I really enjoyed this