National Pi Day

For a fascinating look at π (sorry about the weird font here), enjoy Petr Beckmann's The History of Pi.

One of the most delightful mathematical unities is e^iπ + 1 = 0, connecting 5 fundamental constants. This comes up in theory of complex variables and in electrical engineering. If Lu Chao recited some 67,000 digits in 24 hours, just do the arithmetic to figure out how long it would take for Andriy Slyusarchuk to recite 30 million digits. Not bloody likely, I would guess.

Douglas R. Hofstadter (Godel, Escher,Bach and Metamagical Themas, both excellent books) had a circle of geek friends who would occasionally recite 100 digits of π in unison. I can manage only maybe 9 or 10 on a good day. (I used to know Tom Lehrer's song The Elements, too, but I'm way out of practice these days. There's antimony, arsenic, aluminum, selenium, etc.)

By calculating inscribed and circumscribed 48-gons, Archimedes proved that 3¹⁰/₇₁ < π < 3¹⁰/₇₀. Pretty remarkable for that long ago.

And then encounter Srinivasa Ramanujan....

I had pumpkin pie in honor of the occasion... MMM.... Pie.....

Here, I'd like to clear the pioneer participations of Ancient Egyptians in discovering the number pi (reference: Wikipedia)

The Great Pyramid of Giza is estimated to have originally been 280 cubits in height by 440 cubits in length at each side. The ratio of 440/280 is approximately equal to 2π.

History The earliest evidenced conscious use of an accurate approximation for the length of a circumference with respect to its radius is of 3+1/7 in the designs of the Old Kingdom pyramids in Egypt. The Great Pyramid at Giza, constructed c.2550-2500 BC, was built with a perimeter of 1760 cubits and a height of 280 cubits; the ratio 1760/280 ≈ 2π. Egyptologists such as Professors Flinders Petrie^[30] and I.E.S Edwards^[31] have shown that these circular proportions were deliberately chosen for symbolic reasons by the Old Kingdom scribes and architects.^[32][33] The same apotropaic proportions were used earlier at the Pyramid of Meidum c.2600 BC. This application is archaeologically evidenced, whereas textual evidence does not survive from this early period.

The early history of π from textual sources roughly parallels the development of mathematics as a whole.^[34] Some authors divide progress into three periods: the ancient period during which π was studied geometrically, the classical era following the development of calculus in Europe around the 17th century, and the age of digital computers.^[35]

Antiquity That the ratio of the circumference to the diameter of a circle is the same for all circles, and that it is slightly more than 3, was known to Ancient Egyptian, Babylonian, Indian and Greek geometers. The earliest known textually evidenced approximations date from around 1900 BC; they are 25/8 (Babylonia) and 256/81 (Egypt), both within 1% of the true value.^[7] The Indian text Shatapatha Brahmana gives π as 339/108 ≈ 3.139.

See also: Chronology of computation of π and Numerical approximations of π

Abdel, I had thought I recalled that the ancient Sumarians had originally recognized the mathematical concept of Pi as well as being the first to split a circle into 360 degrees (their calender had 360 days per year with a five day festival interval in between so they divided a circle up into 360 equal units giving us "degrees"). I had understood that the Egyptians had taken their early rudimentary work and refined it. Not trying to take anything away from the ancient Egyptians, they did some real engineering miracles given their resources (well, that and a large pool of jewish slave labor to draw upon.), but I suspect they stood higher because they stood on the shoulders of others that had come before.

Dear Rorschach,

Please refer to the most trusted international reference of information Wikipedia and see what it said. With my huge respect and great compliment to all world nations.

With my best regards.

Abdel, I cannot find my source for my recollection at the moment, so until I can, I have to withdraw my objection. It is known that some version of Pi was known from textual references as far back as 1900 BC in Greece, Babylonia, India and Egypt which would indicate that either the information originated earlier and had spread fairly widely by that time, or had been discovered independently in multiple locations which seems somewhat unlikely to me. I have not however found the epicenter(s) of that knowledge as yet. The Egyptians WERE the first to use the knowledge in an engineering capacity, so they do deserve props for that.They also would appear to have been the first to implement trigonometry in the form of land surveying thanks to the need to rebuild after each spring's flood of the Nile Valley.

"... and one of these facts is this: By 2,000 B.C., men had grasped the significance of the constant that is today denoted by Π, and they had found a rough approximation of its value."

A History of Pi - Petr Beckmann

http://www.amazon.com/History-Pi-Petr-Beckmann/dp/0312381859

As if the scientific evidence isn't enough, Barsoum has pointed out a number of common sense reasons why the pyramids were not likely constructed entirely of chiseled limestone blocks.

http://www.livescience.com/history/070518_bts_barsoum_pyramids.html

>>>> '............. The ratio of 440/280 is approximately equal to 2π ............'<<<<<<<<

Not even close.... B3

Yes, that is true (440/280 = 2π ), see the first paragraph under the pyramid picture at my post #5:

The Great Pyramid of Giza is estimated to have originally been 280 cubits in height by 440 cubits in length at each side. The ratio of 440/280 is approximately equal to 2π.

Sorry, 440/280 = π/2 not 2 π.

Reducing to lowest terms, 440/280 = 11/7 ≈ 1.571428. π/2 (but not 2π) ≈1.570796. But 22/7 is an early- and well-known approximation to π in the first place.