A Brief History of Pi
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- Rudolph Roberts
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1 Mathπath 2017 Mt. Holyoke College Proof School July 1, 2017
2 We re Catching Up! But first, this update on the score:
3 We re Catching Up! But first, this update on the score:
4 We re Catching Up! But first, this update on the score:
5 We re Catching Up! But first, this update on the score:
6 How Much Is Enough? How many digits of π does a responsible citizen of our modern world need to know?
7 How Much Is Enough? How many digits of π does a responsible citizen of our modern world need to know? 41
8 How Much Is Enough? How many digits of π does a responsible citizen of our modern world need to know? plus the decimal point.
9 Π Boot Camp By the end of this talk you will have memorized all 41 digits.
10 Π Boot Camp By the end of this talk you will have memorized all 41 digits. Let s begin See the digits. (No talking yet)
11 Π Boot Camp By the end of this talk you will have memorized all 41 digits. Let s begin See the digits. (No talking yet) Say the digits. (All together)
12 Π Boot Camp By the end of this talk you will have memorized all 41 digits. Let s begin See the digits. (No talking yet) Say the digits. (All together) Only these digits! (Kids these days)
13 Π Boot Camp By the end of this talk you will have memorized all 41 digits. Let s begin See the digits. (No talking yet) Say the digits. (All together) Only these digits! (Kids these days) OK, that s enough. (More later)
14 Homonymish Can you spot the historical object?
15 Homonymish Can you spot the historical object? Name:
16 Homonymish Can you spot the historical object? Name: Rhind Papyrus Civilization:
17 Homonymish Can you spot the historical object? Name: Rhind Papyrus Civilization: Egyptian Date:
18 Homonymish Can you spot the historical object? Name: Rhind Papyrus Civilization: Egyptian Date: around 1650 BC
19 Homonymish Can you spot the historical object? Name: Rhind Papyrus Civilization: Egyptian Date: around 1650 BC Why did the Egyptians care about area?
20 Fruit Ninja Can you spot the historical object? Name: Rhind Papyrus Civilization: Egyptian Date: around 1650 BC Why did the Egyptians care about area?
21 Calc Like An Egyptian How did the Egyptians calculate the area of a circular piece of land?
22 Calc Like An Egyptian How did the Egyptians calculate the area of a circular piece of land?
23 Calc Like An Egyptian How did the Egyptians calculate the area of a circular piece of land?
24 Calc Like An Egyptian How did the Egyptians calculate the area of a circular piece of land?
25 Calc Like An Egyptian How did the Egyptians calculate the area of a circular piece of land?
26 Calc Like An Egyptian How did the Egyptians calculate the area of a circular piece of land? π
27 Calc Like An Egyptian How did the Egyptians calculate the area of a circular piece of land? π π 3.16
28 Yawn Like a Babylonian How did the Babylonians feel about π?
29 Yawn Like a Babylonian How did the Babylonians feel about π?
30 Yawn Like a Babylonian How did the Babylonians feel about π?
31 Yawn Like a Babylonian How did the Babylonians feel about π? Various sources say that the Babylonians used π 3 or It didn t really matter.
32 Π Boot Camp We ve conquered six digits so far. Here are the next seven: See the digits. (No talking yet)
33 Π Boot Camp We ve conquered six digits so far. Here are the next seven: See the digits. (No talking yet) Say only these digits.
34 Π Boot Camp We ve conquered six digits so far. Here are the next seven: See the digits. (No talking yet) Say only these digits. Once more with feeling.
35 Π Boot Camp We ve conquered six digits so far. Here are the next seven hidden from sight: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now the entire first portion.
36 Geek Like A Greek The preeminent Greek scientist and mathematician was...
37 Geek Like A Greek The preeminent Greek scientist and mathematician was... Archimedes. He used inscribed and circumscribed hexagons to deduce that < π < 31 7, or < π <
38 The Pi Dynasty Not long after, and (most likely) completely independent of Greek influence, Chinese mathematician Liu Hui found five digits of π.
39 Π Boot Camp We ve mastered thirteen digits. Next up: See the digits. (No talking yet)
40 Π Boot Camp We ve mastered thirteen digits. Next up: See the digits. (No talking yet) Say only these digits.
41 Π Boot Camp We ve mastered thirteen digits. Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling.
42 Π Boot Camp We ve mastered thirteen digits. Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now with the previous portion.
43 Π Boot Camp We ve mastered thirteen digits. Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now with the previous portion. (No peeking!)
44 Prof D vs Dr. T In which part of the world did much of the best medieval mathematics occur?
45 Prof D vs Dr. T In which part of the world did much of the best medieval mathematics occur?
46 Prof D vs Dr. T In which part of the world did much of the best medieval mathematics occur? Madhava School
47 Ingenuity In India The Madhava School discovered series for sine and cosine via geometric methods, which led to a series for π, namely π =
48 Ingenuity In India The Madhava School discovered series for sine and cosine via geometric methods, which led to a series for π, namely π = Using an extremely clever error correction step, they computed π to eleven digits.
49 Let s Hear It For Glen! In which part of the world does much of the best history of mathematics occur?
50 Let s Hear It For Glen! In which part of the world does much of the best history of mathematics occur?
51 Let s Hear It For Glen! In which part of the world does much of the best history of mathematics occur?
52 Let s Hear It For Glen! The contribution of Canada to this story lies in correctly identifying all the digits of π. π
53 Let s Hear It For Glen! The contribution of Canada to this story lies in correctly identifying all the digits of π. π π
54 Π Boot Camp We re experts on twenty digits. Next up: See the digits. (No talking yet)
55 Π Boot Camp We re experts on twenty digits. Next up: See the digits. (No talking yet) Say only these digits.
56 Π Boot Camp We re experts on twenty digits. Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling.
57 Π Boot Camp We re experts on twenty digits. Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now with the previous portion.
58 Π Boot Camp We re experts on twenty digits. Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now with the previous portion. (No peeking!)
59 For π, I Ran to Iran Only 25 years after the achievement of the Madhava School, Jamshid Al-kashi in Iran shattered all previous records by computing, with proof, sixteen digits of π.
60 π in Print In 1706 the Welsh mathematician William Jones used the symbol π to represent half the perimeter (or periphery) of a unit circle.
61 π in Print In 1706 the Welsh mathematician William Jones used the symbol π to represent half the perimeter (or periphery) of a unit circle.
62 π in Print In 1706 the Welsh mathematician William Jones used the symbol π to represent half the perimeter (or periphery) of a unit circle.
63 π in Print In 1706 the Welsh mathematician William Jones used the symbol π to represent half the perimeter (or periphery) of a unit circle. π = 2 ( ) 27 +
64 π in Print In 1706 the Welsh mathematician William Jones used the symbol π to represent half the perimeter (or periphery) of a unit circle. π = 2 ( ) 27 + π = 4( )
65 π in Print In 1706 the Welsh mathematician William Jones used the symbol π to represent half the perimeter (or periphery) of a unit circle. π = 2 ( ) 27 + π = 4( ) tan 1 x = x 1 3 x x5 1 7 x7 +
66 π in Print
67 Machin π Great Again Jones is referring to an electrifying recent development in π computation made that same year by John Machin, who observed ( ) ( ) π = 4 tan 1 tan Recall that he had the formula tan 1 x = x 1 3 x x5 1 7 x7 +
68 Machin π Great Again In 1873 William Shanks used Machin s identity to compute π to 707 digits.
69 Machin π Great Again In 1873 William Shanks used Machin s identity to compute π to 707 digits.
70 Π Boot Camp We re getting behind! Next up: See the digits. (No talking yet)
71 Π Boot Camp We re getting behind! Next up: See the digits. (No talking yet) Say only these digits.
72 Π Boot Camp We re getting behind! Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling.
73 Π Boot Camp We re getting behind! Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now with the previous portion.
74 Π Boot Camp We re getting behind! Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now with the previous portion. (No peeking!)
75 πroliferation Suddenly everyone was discovering clever formulas for π, calculating hundreds of digits, or both. Here are some of my favorites: π 3 4 =
76 πroliferation Suddenly everyone was discovering clever formulas for π, calculating hundreds of digits, or both. Here are some of my favorites: π 2 = ( ( ( ))) 3 5 7
77 πroliferation Suddenly everyone was discovering clever formulas for π, calculating hundreds of digits, or both. Here are some of my favorites: π 1 =
78 πroliferation Suddenly everyone was discovering clever formulas for π, calculating hundreds of digits, or both. Here are some of my favorites: 4 π =
79 Back to Canada Ramanujan deduced the mind-boggling 1 π = 2 2 (4n)!( n), 9801 (n!) n n=0 which give after just one term
80 Back to Canada Ramanujan deduced the mind-boggling 1 π = 2 2 (4n)!( n), 9801 (n!) n n=0 which give after just one term π In your own lifetime, Canadian mathematicians Jon and Peter Borwein have vastly generalized this sort of formula.
81 Billions and Billions Served The Chudnovsky brothers were the first to reach one billion digits in 1989.
82 Billions and Billions Served The Chudnovsky brothers were the first to reach one billion digits in The current record is over 68 billion digits, held by Kanada and Takahashi.
83 Billions and Billions Served The Chudnovsky brothers were the first to reach one billion digits in The current record is over 68 billion digits, held by Kanada and Takahashi. So what is the billionth digit of π?
84 Billions and Billions Served The Chudnovsky brothers were the first to reach one billion digits in The current record is over 68 billion digits, held by Kanada and Takahashi. So what is the billionth digit of π? I m not entirely sure, but perhaps
85 Π Boot Camp We re almost there! Next up: See the digits. (No talking yet)
86 Π Boot Camp We re almost there! Next up: See the digits. (No talking yet) Say only these digits.
87 Π Boot Camp We re almost there! Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling.
88 Π Boot Camp We re almost there! Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now with the previous portion.
89 Π Boot Camp We re almost there! Next up: See the digits. (No talking yet) Say only these digits. Once more with feeling. Now with the previous portion. (No peeking!)
90 Prof D vs Dr. T Rematch In which part of the world did the most ludicrous episode in the history of π occur?
91 Prof D vs Dr. T Rematch In which part of the world did the most ludicrous episode in the history of π occur?
92 Prof D vs Dr. T Rematch In which part of the world did the most ludicrous episode in the history of π occur? π is the law
93 Moment of Truth
94 Moment of Truth Can we do it?
95 Moment of Truth Can we do it? YES WE CAN!
96 That s Really All Have a superb ole weekend!
97
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