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Pi Day
By Shlomo Maital
Yesterday, Friday, was Pi Day. March 14. 3.14 Warning: This blog has a lot of numbers.
Yes, I did bake an apple pi — for our synagogue’s pot luck supper. And yes, I added home made vanilla ice cream to top it.
Pi is 3.141592653,… It is the ratio of the circumference of a circle to the diameter.
Why is it called by the Greek letter pi? To represent: Perimeter. Pi.
Engineers say in practice, e.g. building bridges, you never need pi to more than 10 digits….yet, mathematicians have calculated pi to (wait for it) — As of July 2024, π has been calculated to 202,112,290,000,000 (approximately 202 trillion) decimal digits.
I asked ChatGPT how many print pages would it take to print out all 202 trilliong decimals. Here is its answer:
Calculation:
202,112,290,000,000 digits: 1250 digits per page\frac{202,112,290,000,000 \text{ digits}}{1250 \text{ digits per page}}1250 digits per page202,112,290,000,000 digits =161,689,832,000 pages= 161,689,832,000 \text{ pages}=161,689,832,000 pages ≈ 161.7 billion A4 pages.
OK – I asked it, so how many trees would it take, to make the paper, to print all 212 trillion digits on A4 pages? Here is ChatGPT’s answer. In 3 seconds.
Calculation:
161,689,832,000 pages8,500 pages per tree\frac{161,689,832,000 \text{ pages}}{8,500 \text{ pages per tree}}8,500 pages per tree161,689,832,000 pages =19,022,333,176 trees= 19,022,333,176 \text{ trees}=19,022,333,176 trees
≈ 19 billion trees 🌳
How Big is That? ChatGPT says:
- “The Amazon Rainforest has an estimated 390 billion trees.
- Printing π to 202 trillion digits would require about 5% of all the trees in the Amazon.
- The total number of trees on Earth is estimated at 3 trillion.
- This means we’d need 0.63% of all trees on Earth just for this print job!
So… maybe it’s best to keep π digital instead. 😅🌍♻️ “
- – – – – – –
Wait a second. Get that last comment! “Maybe it’s best to keep pi digital instead.” With emojis! ChatGPT has a sense of humor!
It’s almost …. Human.
It will take me a while to process that.
Happy Pi Day.
One last comment. Archimedes calculated pi in 220 B.C.E. very precisely. How? By a brilliant method.
He drew a big circle with radius 1. He drew within it a polygon (equal sided figure) inscribed, with 96 sides and calculated the sum of the length of the 96 sides, using Pythagoras’ theorem. (Each side of the polygon is a hypotenuse of a triangle). This is the low estimate of pi.
Next, he drew another polygon with 96 sides, on the outside of the circle, each side tangential or touching the circle. Again, he measured the sum of the length of the 96 sides. This is the high estimate.
Finally: He calculated: the smallest value of pi is the length of the 96 sides inscribed in the circle, or 3 1/7, or 3.142857; and the biggest value of pi is the length of the 96 sides circumscribed on the circle (outside it), or 3 10/71, 3.140845. The average of the two is 3.141851.
True value: 3.14159.
Archimedes’ value for pi is 1.000083079 of the true value.
So, we spent the next 2,255 years calculating more pi digits than we could possibly need.
Why? Same reason Trump closes the Department of Education.
Because – he can.
TIMnovate 