Thread by @rjallain

MEGA THREAD. Happy #PiDay to everyone.

Let's start with the simplest calculation of Pi - the ratio of circumference to diameter for round objects. wired.com/2014/03/calcul…

2/ If you want to do this calculation of Pi, just find a bunch of circular objects of different size. Use a string to wrap around and measure the circumference and then measure the diameter. Plot C vs. d - the slope is PI.

3/ But wait! #PiDay is only Pi in the USA where we use date format of month/day/year.

For everyone else, today is 14/3/2019 - which is NOT Pi. I suggest the other Pi day is July 22 (22/7/2019) since 22/7 is a great fractional representation of Pi. wired.com/2011/03/what-i…

4/ Now for THE BEST way to calculate Pi - with random numbers. Generate two random numbers between 1 and 0 and let that be (x,y) coordinates. Now plot these. If x^2 + y^2 is less than 1, make it a blue dot. Otherwise, red.

5/ The red dots make the area of a quarter of a circle (the aspect ratio is off in the graph). So the ratio of the number of red dots to the total dots can give you Pi. wired.com/2017/03/lets-c…

The is the Monte Carlo calculation of Pi - since it depends on random numbers

6/ The code for this is super simple - here, check it out.

trinket.io/glowscript/8d2…

@GlowScript_Code @gopicup @trinketapp

7/ Of course if you want to use this method to get a good value of Pi, you need LOTS OF RANDOM NUMBERS

wired.com/images_blogs/w…

8/ How about something crazy? What if you use the digits of Pi as a random number generator to use for Monte Carlo? Are the digits of Pi even random?

wired.com/2012/03/can-yo…

9/ As long as we are talking about random numbers - you can also find the value of Pi with a random walk in 1 dimension (actually, it works in higher dimensions too).

wired.com/2017/03/hey-ca…

10/ What does Pi have to do with gravity? Pi^2 is approx = 9.8 (which is g = 9.8 N/kg). Why?

It's because the original measurement of g used a pendulum 1 meter long.

wired.com/2013/03/what-d…

11/ That means that if you know the value of g, you can use the period of a pendulum to calculate Pi.

wired.com/2013/03/can-yo…

12/ If you can use a pendulum to measure Pi, then you can also use a mass oscillating on a spring - in fact, this way doesn't even need the value of g.

wired.com/2011/03/how-do…

13/ Pi is one of those 5 super weird numbers in the Euler Identity

wired.com/2016/03/six-th…

14/ If you can use the circumference of a circle to find pi, you can also use the area of a circle. Measuring the area of a circle can be tricky - so I just cut some circles out of paper and measured the mass.

wired.com/2015/03/area-c…

15/ If you wanted to represent Pi as a fraction, what is the best possible fraction you could use?

wired.com/2011/03/findin…

16/ You can also calculate Pi by integrating to find the area of a circle - but this is a numerical integration using python.

wired.com/story/this-pi-…

@GlowScript_Code @gopicup

17/ the code for this numerical integration really isn't that complicated. Also, I think doing a numerical calculation can help people understand analytical integration.

18/ If you let two balls of different mass collide elastically and then let one of those balls bounce off a wall, you can get the digits of pi by counting the number of collisions.

wired.com/story/for-pi-d…

19/ Instead of explaining WHY this colliding ball thing works, I show you HOW to model this in python.

20/ Ok, that's enough of Pi day for now. I'll add more next year.