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Doctor Q

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Here is an animated gif from tenor.com in memory of Steve Wilhite, who invented the GIF (graphics interchange format) file format in 1987 when he worked at early Internet service CompuServe. He died on Pi Day 2022.

pi-day-314.gif
 

Doctor Q

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Sep 19, 2002
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Bases loaded

If you think that pi is 3.14159265358... then it's probably a sign that you have 10 fingers.

There's nothing special about base 10 other than it being convenient for people with the typical number of fingers (or toes, if you count that way).

But what if you have a different number of fingers? When you count on your fingers, it's in one of these bases:

𝝅 = 11.0010010000... in base 2
𝝅 = 1.00102110122... in base 3
𝝅 = 3.02100333122... in base 4
𝝅 = 3.03232214303... in base 5
𝝅 = 3.05033005141... in base 6
𝝅 = 3.06636514320... in base 7
𝝅 = 3.11037552421... in base 8 (just don't include your thumbs)
𝝅 = 3.12418812407... in base 9
𝝅 = 3.14159265358... in base 10
𝝅 = 3.16150702865... in base 11
𝝅 = 3.184809493B9... in base 12
𝝅 = 3.1AC1049052A... in base 13
𝝅 = 3.1DA75CDA813... in base 14
𝝅 = 3.21CD1DC46C2... in base 15
𝝅 = 3.243F6A8885A... in base 16
𝝅 = 3.26FAG579ED6... in base 17
𝝅 = 3.29FDEH0G771... in base 18
𝝅 = 3.2D23982975G... in base 19
𝝅 = 3.2GCEG9GBHJ9... in base 20

I'm using A for digit 10, B for digit 11, and so on.

If you have more than 20 fingers, try counting on only one hand.
 

chown33

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Aug 9, 2009
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Bases loaded

If you think that pi is 3.14159265358... then it's probably a sign that you have 10 fingers.

There's nothing special about base 10 other than it being convenient for people with the typical number of fingers (or toes, if you count that way).

But what if you have a different number of fingers? When you count on your fingers, it's in one of these bases:

𝝅 = 11.0010010000... in base 2
𝝅 = 1.00102110122... in base 3
𝝅 = 3.02100333122... in base 4
𝝅 = 3.03232214303... in base 5
𝝅 = 3.05033005141... in base 6
𝝅 = 3.06636514320... in base 7
𝝅 = 3.11037552421... in base 8 (just don't include your thumbs)
𝝅 = 3.12418812407... in base 9
𝝅 = 3.14159265358... in base 10
𝝅 = 3.16150702865... in base 11
𝝅 = 3.184809493B9... in base 12
𝝅 = 3.1AC1049052A... in base 13
𝝅 = 3.1DA75CDA813... in base 14
𝝅 = 3.21CD1DC46C2... in base 15
𝝅 = 3.243F6A8885A... in base 16
𝝅 = 3.26FAG579ED6... in base 17
𝝅 = 3.29FDEH0G771... in base 18
𝝅 = 3.2D23982975G... in base 19
𝝅 = 3.2GCEG9GBHJ9... in base 20

I'm using A for digit 10, B for digit 11, and so on.

If you have more than 20 fingers, try counting on only one hand.
In base pi, it's 1.00. Because everything should be counted in semicircles.
 
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chown33

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Aug 9, 2009
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That explains the circle around your avatar.
It's not really a circle, only an approximation using a series of 4 cubic splines.

For example, in the "Joker lantern" avatar I use in October, here's the PDF fragment that makes the solid orange "almost circle":
Code:
 1.000 0.588 0.000 rg
 370 200.0 m
 370 293.803  293.803 370  200.0 370  c
 106.197 370  30 293.803  30 200.0  c
 30 106.197  106.197 30  200.0 30  c
 293.803 30  370 106.197  370 200.0  c
 f
That's the approximation for a circle centered at 200,200 in a 400x400 box, with a radius of 170.

Joker-lantern-200.png
 

Doctor Q

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Sep 19, 2002
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Los Angeles
The last digit of pi is 6!

Well, perhaps I didn't phrase that correctly. What I meant to say is that the last digit of pi that's been computed so far is 6.

After 75 days of computing, storage vendor Solidigm announced that they had set a new world record by computing pi to 105 trillion decimal digits, the last of which is 6. This beats the previous record, a mere 100 trillion digits.
 
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chown33

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Aug 9, 2009
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Now I have to work out what circumference we'd need in order for that level of precision to produce an error of 1mm. I have a feeling it would handily exceed the circumference of the observable universe. Probably even if that circumference were measured in Planck lengths instead of mm.
 
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