How You Can Use Polygons to Approximate Pi
ฝัง
- เผยแพร่เมื่อ 28 ก.ย. 2024
- This is a little bonus video about a simple way to prove that pi is between 3 and 4, and why similar techniques were used by ancient mathematicians. Make sure you've also seen my latest main episode on my @ComboClass channel: • The Mysterious Pattern...
Links:
Main channel: / comboclass
Patreon: / comboclass
Subreddit: / comboclass
[I need to get an updated link to the Discord which I accidentally logged out of a while ago and haven't been on recently. I'll add that back to my video descriptions soon].
Combo Class, taught by me (Domotro), is a crazy educational show where you can have fun learning rare things about math, science, language, and more! This is actually kind of my "bonus" channel for my livestreams, shorts, and extra content - make sure you're also subscribed to the main @ComboClass channel where my main episodes go!
DISCLAIMER: any use of fire, tools, eating unexpected things, or other dangerous-seeming actions in this series are experiments that are conducted safely and professionally, and/or are accidents that I include in the videos for educational purposes. Do NOT try to copy any experiments (or accidents) that you see in these videos yourself.
I filmed a few more bonus videos like this (and some shorts) which will come out in the next few days. Also make sure you've seen my latest main episode on my @ComboClass channel: th-cam.com/video/pylw9t4j6bM/w-d-xo.html
You win the internet sir salute. I am also interested in the quantum frontier and if it can be used for the star trek stuff. Neutrino something something some angle of something.
it seems important to me that the ratio between a chord, that is the side of an inscribed polygon, and its arc is .
You can go one step further easily. The radius of the circle bisects the hexagon. We can draw a 1/2, 1, ? right angle triangle to find the length of the bit of the radius that's inside the circle, then take that from the radius as a whole (from 1) to get the length of the bit outside by pythagoras. We can then make a right triangle from the 1/2 of the hexagon (1/2) and that newly found length, to find the hypotenuse by pythagoras. This gets us 98% of the way to Pi if we add up the outer triangle sides!
I've been trying to find a way to get closer with polygons but i can't. I like this because it gives a reason WHY the number is 3 point something
Whoa, the lab coat has shapes on it now
good video
"Were going to use polygons"
"Any polygons or regular polygons?"
"Regular polygons"
Even if intuitively obvious, formally proving that the square has a larger circumference than the inscribed circle is not entirely trivial, it seems...
Thank you for this episode - i have clicked the 667th like :)
0:09 - as i read all the comments it seems that nobody has expected that fall this year :)
I have a nice and quick method of mathematically, practically approximating PI using polyhedrons :) (polyhedrons are made of many polygons so it should be ok?...)
1st you take a highly composite number of grains of sugar - like 360 or 5040 if you like bigger numbers
2nd you take a flat round pan with a very thin layer of dense substance on the sutface like butter or honey and with high edges
3rd you draw a hexagon inscribed in that pan/circle
4th after throwing the sugar particles from high above you count how many of them fit into the {CiRCLE minus HEXagon surface} and how many missed the pan edges/ fell off - short count - roughly 1/5 need to be counted
5th youve got a 1 / 5 * SQRT(HCN chosen) exact approximation of a formulae of 2 * PI / 3 * SQRT(3)
6th You make a video about aproximating SQRT(3) :)
7th - You take a look at Chudnovsky algorithm and wonder why in Gauss system CGS the magnetic permeability of vacuum is 4 PI x 10E-7 and why physicist have it all easier
This method sounds... exhausting 😃
I am here from you livestream today, thanks for dropping another video :)
Thumb pointing North emoji
Keep it up, man!⚔️