Fractal Snowflakes, Symmetries, and Beautiful Math Decorations
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- Опубліковано 2 чер 2024
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Today is MATH CRAFTS day! We're going to make some holiday decorations and then also chat about the cool math behind them. We'll learn about the cool Koch Snowflake fractal (infinite perimeter but finite area!), the dihedral group symmetries of the snowflakes, and finally an origami stellated dodecahedron.
0:00 The Koch Snowflake algorithm
1:16 Crafting a Koch Snowflake
1:59 Mathematical properties of the Koch Snowflake
6:02 Symmetries of Snowflakes
9:18 The Dihedral Group
11:22 Origami Dodecahedron
12:43 Brilliant.org/TreforBazett
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Last video of the year!! Thanks everyone for the awesome ride in 2022, UA-cam has such an amazing math community:)
And of course I have to bug you all to check out our sponsor brilliant.org/TreforBazett who have been really great to me this past year and looking forward to working with them more in 2023. See you all then!
My favorite fractal is the Sierpinski triangle, because it's an infinite triforce!
Koch Snowflake and smoking crystal math
Hey Trefor. I just got a perfect score on my diff eq final. I definitely could not have done it without your diff eq playlist. You have a gift for explaining for complicated concepts in a way that is easy to understand, but not oversimplified.Thank you so much!
I’m so happy to hear that!
The finite area / infinite perimeter property also holds for some non-fractal shapes too! e.g. Gabriel's horn (the surface of revolution of y = 1/x from x=1 to infinity) which has finite volume but infinite surface area
Totally! I actually have a video on that one:)
Cool adding some modular origami!
WARNING
Building the snowflake by gluing on triangles always stays withing a circle around the original triangle. However it becomes infinitely thick and dangerously sharp. Recomended to build it outdoors and wear gloves (or, to be boring, restrict yourself to a finite number of iterations).
Saving me from failure during the year and from boredom during break. I love this man
I'll definitely be making these to decorate my tree
Nice!
In the snowflake you showed the 3 axis of symmetry. Are there not also another 3 axis of symmetry halfway between each of those? ❄️
Yes! I think I said verbally there were six but somehow that snowflake with its six points harder to draw the lines for other three.
My goto reference for building maths things is:
Mathematical Models by H. M. Cundy and A. P. Rollett
Just checked - too much dust on it - time to reread and build.
Do like your method of building the snowflake - must try that, which grandchildren can I persuade to help me?
wow..that snowflake idea for dihedral groups was pretty cool... i used dice, but the reflections were a bit harder to grasp...(d&d nerd here)
Now, can you make a hyperbolic snowflake?
Ya I really like that you can actually fold them and see it matches. Hyperbolic would be fun!
bravo!
I have build the Menger Sponge and the Mosely Snowflake Sponge Fractals from business card sized pieces. The Mosely Snowflake Sponge I posted a video of on my channel.
1:56, the second red triangle, i.e., the first iteration, should have been a different color.
If the perimeter is infinite then in gaming terms this will never be rendered by our current graphics cards due to the insane detail in texture xD
Sir ,have you uploaded the this type lecture for ""Mothed of substitution to evaluate the integral of the trigonometry """ like integral 1÷a^2-x^2
you just set a new thumbnail and I instantly clicked the video
haha my plan is working lol:D But seriously last thumbnail wasn't working for some reason:D
Same me!!
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Is there a shape you can rotate by 360 degrees and it's NOT the shape you started with?
Hello, good day Dr. Trefor Bazett! I am Jonibek Abdullayev!
First of all, sorry to bother you. Happy New Year. I am your follower on social networks. Please help me to draw a graph from complex analysis in the Latex template. I will send some files to you. I would be very grateful if you could help me. With sincere regards and respect,
Jonibek.
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