Algebra vs Geometry in Trigonometry | DIw/oI #3 @mathemaniac

Mathemaniac | Algebra vs Geometry in Trigonometry | DIw/oI #3 @mathemaniac | Uploaded 5 years ago | Updated 3 hours ago
Previous video: youtu.be/8I5hbthISt8

The idea for this video came up suddenly while writing the script for the previous video. A trigonoemtric identity can be derived using algebra or geometric methods, and you can see which one you like in this video!

The content is extracted from Trigonometric Delights by Eli Maor, which is an incredible book for recreational Mathematics.

Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels:
https://forms.gle/QJ29hocF9uQAyZyH6

If you want to know more interesting Mathematics, stay tuned for the next video!

SUBSCRIBE and see you in the next video!

#mathemaniac #math #trigonometry #battle #algebravsgeometry #algebra #geometry

Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory

Complex integration, Cauchy and residue theorems | Essence of Complex Analysis #6

$What do Fibonacci numbers have to do with combinatorics? Part II: https://youtu.be/_RHXmGWXUvw Note: You ABSOLUTELY DONT NEED TO HAVE KNOWN ANY COMBINATORICS because the combinatorics required in this video would be explained thoroughly. Source of the beautiful thumbnail: https://www.videoblocks.com/video/winter-stargate-deep-space-fibonacci-spiral-infinite-zoom-scl2tvcpliylych5s Usually we dont associate Fibonacci numbers with combinatorics (binomial coefficients), but here is a surprising relationship between the two, using the generating function of Fibonacci numbers. Other useful links: https://www.quora.com/How-would-you-show-that-sum-limits k-1-infty-frac-F k-x-k-frac-x-x-2-x-1/answer/Trevor-Cheung https://www.johndcook.com/blog/2018/02/22/fibonacci-binomial-coefficient-identity/ (the comment is worth reading) https://proofwiki.org/wiki/Fibonacci_Number_as_Sum_of_Binomial_Coefficients#Proof (A bit more rigorous proof of the relation shown, only if you are comfortable with all the binomial coefficients involved) Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! #mathemaniac #math #combinatorics #fibonacci #generatingfunction #binomialcoefficients$

Why study Lie theory? | Lie groups, algebras, brackets #1

15-year-old did mathematical research?! What was my thinking process back then?

Why care about complex analysis? | Essence of complex analysis #1

4 DIFFERENT ways to prove Herons formula

Chapter 5: Quotient groups | Essence of Group Theory

The 5 ways to visualize complex functions | Essence of complex analysis #3

$Everything you need to know about operations in modular arithmetic First video ever: https://youtu.be/oOsYACy0UUY Previous video (LaGrange and Chinese remainder theorem): https://youtu.be/iIV9tdmWYmU Congruence relations only work for integers, so can we do division on them? The answer is more complicated than you think - well no, but actually yes. We need to consider a lot more cases including whether some numbers are coprime. Note: Most people would learn Euclidean algorithm and its reverse or extension to work out the multiplicative inverse. It is exactly identical to what I have shown here - continued fraction expression is equivalent to Euclidean algorithm; using the property is equivalent to Extended Euclidean algorithm; directly expanding the second-to-last continued fraction convergent is equivalent to Euclidean algorithm in reverse. Useful link: https://www.quora.com/q/igcnjlpcjdmjyiqa/Chinese-a-remarkable-achievement-in-modular-arithmetic Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! #mathemaniac #math #modulararithmetic #division #continuedfraction$

Cosine law and properties of cyclic quadrilaterals