Tetration: The operation you were (probably) never taught
We've all done addition and multiplication, and maybe even exponentiation. But what comes after? Is there more?
In this episode, we look into Tetration, a fun example of how a pattern that had been sitting right under your nose for a very long time might be explored!
Note: This is a re-uploaded video after fixing an issue pointed out by a user. Thanks again for the correction!
Yet another note: Holy mackrel I love you guys. There's yet ANOTHER minor detail I goofed up; it should be 1.9*10^2184, not 1.9*10^2185. Typos are a thing (see: the dangling parenthesis hidden somewhere in the video).
Link to the original Perlin Noise Video: https://youtu.be/ZsEnnB2wrbI
Link to Part 1 of this series: https://youtu.be/khayN87yKYQ
Link to Part 2 of this series: https://youtu.be/pxOjHsEAd0g
If you want more Blender tutorial content, geared towards math education, let me know in the comments!
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Over the past few years, I have gotten an enormous amount of value, personally as a creator, from the vast community of content creators making Blender tutorials. My goals with the software relate to using it for making math education videos for the Taylor Series (and a few other unrelated creative projects).
Well, I'd like to give something back!
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Useful Perlin Noise Links:
Code Behind Perlin Noise: https://rtouti.github.io/graphics/perlin-noise-algorithm
Understanding Perlin Noise: https://adrianb.io/2014/08/09/perlinnoise.html
A good glossary for terms related to noise: http://libnoise.sourceforge.net/glossary/#lacunarity
Dot Product resource: https://betterexplained.com/articles/vector-calculus-understanding-the-dot-product/
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Links to other amazing Blender tutorial makers:
CG Matter: https://www.youtube.com/c/CGMatter
Blender Guru: https://www.youtube.com/c/BlenderGuruOfficial
Erindale: https://www.youtube.com/c/Erindale
Blender Secrets: https://www.youtube.com/c/BlenderSecrets
Curtis Holt: https://www.youtube.com/c/CurtisHolt
Ducky 3D: https://www.youtube.com/channel/UCuNhGhbemBkdflZ1FGJ0lUQ
Polyfjord: https://www.youtube.com/c/Polyfjord
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The Taylor Series aims help people love math. Whether you're a student in a math class or someone who has ever asked the question, "What was the big deal about Calculus?" there's something here for you.
Also, I named this the Taylor Series after the mathematical construct created by James Gregory and formally introduced by Brook Taylor ... and I picked this one in particular because my name is Derrick Taylor. :)
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Patreon: https://www.patreon.com/TaylorSeries
Facebook: https://www.facebook.com/TheTaylorSeries
Twitter: @TheTaylorSeries
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Software Used: Windows 10, OBS, Unity, Blender, Adobe Premiere Pro, Adobe After Effects, Adobe Audition, Google Drive (for script)
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Credits:
Intro Music:
Japan by Uniq | https://soundcloud.com/uniqofficial/
Music promoted by https://www.chosic.com/free-music/all/
Attribution 4.0 International (CC BY 4.0)
https://creativecommons.org/licenses/by/4.0/
All other music is from Audioblocks
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https://www.youtube.com/watch?v=CXHRJdq4OjA
In this Taylor Series Tidbit, you will learn how to add two natural numbers (that is, positive whole numbers) that are greater than 10!
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Parent video: https://www.youtube.com/watch?v=0poh3w_Vm_A
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The Taylor Series aims to teach math. Whether you're a student in a math class or someone who has ever asked the question, "What was the big deal about Calculus?" there's something here for you.
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https://www.youtube.com/watch?v=4s7i0ht5cyI
I rarely ask this, but please share this video!
This is a more serious video than my usual fare. But, understanding better how the math behind these epidemics work can help inform us about what's to come and what we can do.
A short bit of background, if you'll indulge me. I have been wanting to make a video on this topic, but things moved so quickly that each time I started a version of this, current events outpaced me. So, I cranked this out in a single day from writing to filming to editing to publishing! As a result, some of the audio is a bit messed up, and there are fewer animations and gags. But, the math is still good, so I hope you'll take something away.
Hopefully, I don't have any typos this time (disclaimer: I always hope this; it does me no good).
Extra Special Thanks to Brad Heller for helping me iron out this video!
My Exponentials video (with Thanos): https://youtu.be/727buOqGFco
I used Desmos for graphing things: www.desmos.com
Some interesting links:
https://www.washingtonpost.com/graphics/2020/world/corona-simulator/
https://medium.com/@tomaspueyo/coronavirus-act-today-or-people-will-die-f4d3d9cd99ca
https://web.stanford.edu/~jhj1/teachingdocs/Jones-on-R0.pdf
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The Taylor Series aims help people love math. Whether you're a student in a math class or someone who has ever asked the question, "What was the big deal about Calculus?" there's something here for you.
Also, I named this the Taylor Series after the mathematical construct created by James Gregory and formally introduced by Brook Taylor ... and I picked this one in particular because my name is Derrick Taylor. :)
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Patreon:
https://www.patreon.com/TaylorSeries
Facebook:
https://www.facebook.com/TheTaylorSeries
Twitter:
@TheTaylorSeries
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Music Credits (from AudioBlocks):
Intro music: Thinking by Patrick Smith
Main background music: Island Fun by Neil Cross
Outro music: Midnight City Lights by Neil Cross
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https://www.youtube.com/watch?v=TpgT2ZTuftU
In today's Vlog, I outline how to deal with scenarios wherein you get the right answer from the wrong work. :)
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The Taylor Series aims help people love math. Whether you're a student in a math class or someone who has ever asked the question, "What was the big deal about Calculus?" there's something here for you.
I am aiming to have one new video up every month. I hope you enjoy them!
Also, I named this the Taylor Series after the mathematical construct created by James Gregory and formally introduced by Brook Taylor ... and I picked this one in particular because my name is Derrick Taylor. :)
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https://www.youtube.com/watch?v=ufgUcBEEsic
Today, we discover what is meant by mathematicians when they say the word "Variable" by revisiting a weird little moment from my past. :) This is part of my course on Algebra, which I hope you will find useful.
Algebra is a skill fundamental to many math skills beyond arithmetic.
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The Taylor Series aims help people love math. Whether you're a student in a math class or someone who has ever asked the question, "What was the big deal about Calculus?" there's something here for you.
I am aiming to have one new video up every month. I hope you enjoy them!
Also, I named this the Taylor Series after the mathematical construct created by James Gregory and formally introduced by Brook Taylor ... and I picked this one in particular because my name is Derrick Taylor. :)
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Patreon:
https://www.patreon.com/TaylorSeries
Facebook:
https://www.facebook.com/TheTaylorSeries
Twitter:
@TheTaylorSeries
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Music Credits (from AudioBlocks):
Intro music: Thinking by Patrick Smith
Main background music: Island Fun by Neil Cross
Outro music: Midnight City Lights by Neil Cross
...
https://www.youtube.com/watch?v=vq7-jVxF9Ao
Not all infinities are the same size, surprisingly enough! This counterintuitive result has been the source of much consternation. Georg Cantor first discovered this in the 1870s, and the results have influenced many aspects of advanced mathematics ever since. Join me as we explore this interesting fact, and why it's true!
Link to 1st video referenced: https://www.youtube.com/watch?v=tMtDViVhAVE
Link to 2nd video referenced: https://youtu.be/bLKKn_keYhA
More stuff to look up: Set Theory, Axiom of Choice, Continuum Hypothesis, Hilbert Problems, Aleph Numbers, Beth Numbers
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https://www.youtube.com/watch?v=FPBcQowmkPM
Things are happening! I've got a lot of irons in the fire and some fun things coming up soon. Also, look out for a poll; I need some random numbers from you!
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The Taylor Series aims help people love math. Whether you're a student in a math class or someone who has ever asked the question, "What was the big deal about Calculus?" there's something here for you.
I am aiming to have one new video up every month. I hope you enjoy them!
Also, I named this the Taylor Series after the mathematical construct created by James Gregory and formally introduced by Brook Taylor ... and I picked this one in particular because my name is Derrick Taylor. :)
---
Patreon:
https://www.patreon.com/TaylorSeries
Facebook:
https://www.facebook.com/TheTaylorSeries
Twitter:
@TheTaylorSeries
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Music Credits (from AudioBlocks):
Background Music: Deep Progressive by Jason Donnelly
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https://www.youtube.com/watch?v=SrwCuARcV-c
There are a lot of reasons that people find math challenging. In this sequence of videos, I wish to help address some of those reasons.
Seeing others easily master topics we find hard can be daunting, but don't let that hold you back. You can do just about anything you set your mind to. The only person you should compare yourself against is your past self!
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Patreon:
https://www.patreon.com/TaylorSeries
Facebook:
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https://www.youtube.com/watch?v=lrf5chbD7mM