How can you approximate Pi using Geometry?
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- čas přidán 8. 05. 2018
- Approximating Pi was a favourite pastime of many ancient mathematicians, none more so than Archimedes. Using his polygon approximation method we can get whole number bounds of 3 and 4 for the universal constant, with only high-school level geometry.
This is the latest question from Tom Rocks Maths and I Love Mathematics - answering the questions sent in and voted for by YOU.
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Q1: What is the probability I have the same PIN as someone else?
Q2: How long would it take to sink to the bottom of the ocean?
Q3: What is the gravitational field of a hollow Earth?
Q4: What is the best way to win at the board game Monopoly?
Q5: What are the most basic Mathematical Axioms?
Q6: How does Modular Arithmetic work?
Q7: What is the Gamma Function?
Q8: How many ping-pong balls would it take to lift the Titanic from the ocean floor?
Q9: What is the graph of x^x?
Q10: How can you show geometrically that Pi is between 3 and 4?
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This is such a pure way of understanding mathematics. A very good place to start one's journey.
When you mentioned polygons, I tried to do it myself and did it EXACTLY like you did it (outside square with area and inside hexagon with perimeter)
Awesome - well done!
Hey there I have some important questions that I would like you to answer :-1. Why are two negatives =to a positive ..i mean i get that 5-(-)5=10 but how do you understand through a number line?
2.Why does any number raised to the power of 1/2= it's square root
3. Why does a number raised to a negative power equal to it's reciprocal with the denominator raised to its respective positive power?
HOPE U COULD HELP ME OUT. IT WOULD BE GREAT IF U COULD! :)) KEEP UP THE MATH VIDEOS:))))
Hi Amy - great questions. Most of these come from how we 'define' certain operations. For example, for the square root, the idea is that a number to the power 2 means to multiply by itself, so if we take the inverse of 2, which is 1/2 by the law of inverses for a field, then we would want any number to this power to do the 'opposite of squaring'. What this means exactly is open to discussion, but perhaps the most sensible idea is to give the number that when multiplied by itself gets you back to where you started. It's similar to the idea of raising to the power 2, but done in a kind of 'opposite' or 'inverse' way. It's the same idea for questions 1 and 3. Hope that helps!
Thank u fr this amazing information sr......
You're very welcome Vivek.
I love this channel
You guys
Thanks for this video, I will share this method with my students!
Fantastic - thanks Erik!
i love ur videos
Very nice video and also insisting in the idea of the finding "rational" sides in the triangle. Brilliant
glad you enjoyed it :)
Glad you're rise in the youtube trending. I enjoy your content as well as many of the other mathematicians content.
Sorry if I annoyed you guys. I have no mathmatical outlets in my daily life. And never knew calculators had limitations on computations. At least not search engines.
Also found it weird that 2D graphing with pythagorean theorem was the same as plank length math.
IE: a 2-D graph can be used for any unit of measure. Nor taught about 6 sided rectangle cuboids.
These details were never really discussed
But continue the grind.
Thanks Markus :)
regular shape polygon, like 1/1000th segment length of an approximate circle then multiply that by 1000, get the perimeter, directly
y=sqrt(1-x^2), arc segment size, multiply that on some limit, like s->0 or l->0
could you please discuss series involving pi and its proof ?
Added to my list - thanks for the idea.
I liked this video ahem can you tell us why the gamma function is what it is and how people found a pattern
You're in luck - I've already made a video about the Gamma Function here: czcams.com/video/7y-XTrfNvCs/video.html
@@TomRocksMaths why did you skip the part showing how t
you got 2.84??
@@leif1075 what timestamp is that at?
@@TomRocksMaths like at 7:24..and how do you know a triangle with sides 1/2 will fit inside the circle..not the side that is the radius but the other sides..
@@leif1075 for the square (which gives 2.84) we use the fact that the diagonal of the square must be equal to the radius of the circle (1). This should be enough information to work out where 2.84 comes from.
Is 3.14159 is a more accurate pi.
If they where happy with 3.142.
The more accurate you make pi. The more accurate you make 1.2732406202 which equals 4. 1.2732406202 × 3.14159 equals 4.
If 1.2732406202 meter diameter is 1.2732406202 or 3.159 is in meters? Either way the area is 4meters ?