How to Calculate Pi by Throwing Frozen Hot Dogs

I forgot the value of pi during my math exam. So, I snuck out of the exam hall, went to closest grocery store, stole some frozen hotdogs and determined the value of pi using this video. I still failed the exam but thanks for the video

Finally an easy and fast way to calculate Pi, thank you.

we don't need to know wikihow we need to know wikiwhy 💀

this is the type of video to appear in everyones reccomendations like 7 years later

ok 2 things here, first off i didn't even know wikihow had a youtube channel, and second of alll, what the hell

The mathematical explanation on how it works (It's pretty long in text, but actually pretty neat when visualized) BEFORE WE START We're introducing some term and variables to make the explanation more concise. theta : the counter-clockwise angle between the sausage and the horizontal line to the right. Its value ranges from 0° to 180°. To visualize, imagine the sausage as the hour hand of a clock that can be rotated between 9 a.m. to 3 p.m. At 3 p.m. theta is 0°, at 2 p.m. theta is 30°, at 12 p.m. theta is 90°, at 11 a.m. theta is 120°, and so on. d : the length of sausage and distance between horizontal lines. Its value is fixed/constant. y : the distance between the center of the sausage and the closest horizontal line below it. Its value ranges between 0 to d cross : the event of the sausage crossing a horizontal line We're looking at the scene from top view. There are some assumptions: - we are simplifying the sausage and the horizontal strips as one-dimensional lines with no width - theta and y are random and its values are equally likely to occur INTRODUCTION When the sausage lands and stops moving on the floor, we measure the distance *y*. The sausage is oriented at an angle *theta*. When theta is 0° (parallel to the horizontal lines), cross happens when the sausage perfectly landed on top of a horizontal strip. When theta is 90° (perpendicular to the horizontal lines), cross always happens because the length of the sausage is equal to the distance between horizontal lines. In other words, the probability of cross when theta = 0° is 0 (or theoretically infinitely small because we are simplifying the sausage and horizontal strips as 1-dimensional lines with no width). Meanwhile, the probability of cross when theta = 90° is 1 (because it always happens). FINDING THE PROBABILITY FOR A GIVEN ANGLE THETA What about other values of theta ? Let's say theta is 30°. Now imagine a rectangular box with no base or lid, it has only 4 sides whose length you can adjust. The horizontal sides of the box are parallel to the horizontal strips on the floor while the vertical sides are perpendicular. Lastly, we adjust the box size so that it perfectly fits the sausage. Using trigonometry, we can calculate the length of the box's sides that meets these criteria. The vertical sides have a length of d * sin( theta ). Let's give it a name: x . In this case when theta is 30°, x is d * sin(30°) = 1/2 d Now that we have this setup, you can imagine moving around the sausage and the box (while maintaining its orientation). You soon find that cross happens when y is between 0 and 1/2 x or when y is between d - 1/2 x and d . In our case, using the x value before ( theta = 30° ), cross happens when y is between 0 and 1/4 d or between 3/4 d and d . Because we assume y is random and its values are equally likely to occur between 0 and d , the probability of cross is [ ( 1/4 d - 0 ) + ( d - 3/4 d ) ] / d = [ 1/4 d + 1/4 d ] / d = 1/2 To generalize, the probability of cross happening for some value theta is [ ( 1/2 x - 0 ) + ( d - ( d - 1/2 x ) ) ] / d = [ 1/2 x + 1/2 x ] / d = x / d = d * sin( theta ) / d = sin( theta ) PUTTING IT TOGETHER Now, to find the probability of cross happening for all possible values of theta , we use calculus to integrate all the probabilities of cross for all values of theta from 0° to 180° and then divide the result by the probabilities of all possible values of theta . The integral of sin( theta ), with theta from 0° to 180° is -cos( theta ); theta from 0° to 180° = -cos(180°) - (-cos(0°)) = -(-1) - (-1) = 1 + 1 = 2 So the overall probability of cross is 2 / (180° - 0°) we now convert the angles to radiant so we get 2 / (π - 0) = 2 / π BACK TO THE VIDEO This overall probability corresponds to the ratio between the number of crosses and the number of tosses in the experiment. In other words, the probability of cross is (# of crosses)/(# of tosses) We now get the equation (# of crosses)/(# of tosses) = 2 / π Rearranging the equation a bit, we get π = 2 * (# of tosses) / (# of crosses) π = (# of tosses) / [(# of crosses) / 2] CAVEAT To get a better result, you should make sure the experiment condition is as close to the assumptions as possible. The freezing sausage condition helps reduce friction so it can slide and rotate freely. You should also give it a little spin when throwing to give it more randomness. Also, the thinner the sausage and the horizontal strips are, the better. Edit: TLDR Combine trigonometry + calculus + probability + some imagination and *poof* you get the probability of the sausage crossing a line is 2/π. Work it out a little and you get π equals the formula on the video. It works best if the sausage/floor is slippery and you throw it many many times as randomly as possible

Google: Memorise all digits of pi Bing:

If you didn’t know, this is called Buffon’s needle, a fascinating probability experiment devised by the 18th-century French mathematician Georges-Louis Leclerc, Comte de Buffon. In this classic problem, a needle of a certain length is dropped onto a floor marked with equally spaced parallel lines, and the probability of the needle crossing one of the lines is determined. This seemingly simple setup elegantly connects geometry, calculus, and probability theory, and it provides a method for approximating the value of π. By repeating the experiment many times and observing the proportion of times the needle crosses a line, one can gain insights into the nature of random events and the inherent patterns that arise from them

When I saw the title I was just... dead.

Once I heard of this article from a video talking about the strangest wikihow pages, and when I looked on the site, I couldn't find it. Now I finally get a chance to learn how to calculate pi by throwing frozen hot dogs.

Basically it's considered that each hot dog lies with a random angle from 0 to 360 degrees, then calculate the theoretical probability of hot dogs crossing the lines, and there's a pi in the theoretical probability

This GETS me. Everyone yelled at me as a toddler when I threw my toys around. Finally people can believe I was just calculating pi - discovering math.

0:16 can a good personality also work? mine isn't that long

Thank you! I was stuck with only a hot dog and needed to calculate pi, and this saved me!

This is what the internet was made for.

Instructions unclear: I was expelled for doing that on a math exam

I love how this just randomly got recommended to me.

Who has 300 hotdogs just laying around?

Youtube knows that this fella is gonna watch ANYTHING at this point. Why in the world was this recommended to me? 😭

Thank goodness for this tutorial 🙏i can finally calculate Pi by throwing frozen hot dogs