Unlocking the Secrets of Polynomial Expansion: Geometric Insights with Pascal's Tetrahedrons
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- Опубліковано 19 гру 2019
- Join us on an intriguing mathematical journey as we delve into the world of polynomial expansion with a unique twist - geometric interpretations using Pascal's Tetrahedrons. In this captivating video, we explore the formulas needed to efficiently expand polynomials of any size, and unveil how these terms can be related to fascinating geometric figures. Discover hidden patterns and unravel the mysteries of polynomial expansion through an engaging visual approach that will leave you awe-inspired. Whether you're a math enthusiast or simply curious about the beauty of mathematical concepts, this video is a must-watch. Don't miss out on this opportunity to expand your mathematical horizons and uncover new insights into polynomial expansion. Join us now and embark on an illuminating mathematical adventure!
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I was teaching a student about Pascal’s triangle and proposed they consider the situation of (A +B +C)^n … I then thought to myself man I wonder if there’s a video on UA-cam and I am happily surprised .
The fact that the number of vertices/edges/faces etc increase for higher dimensional shapes is mind blowing
Nice to hear the video was interesting for you and your class! Thanks for sharing.
This video is underrated, incredible video thanks.
Thank you! Glad you liked it.
Very helpful! Thank you!
The problem of many math problems is putting something that is visible /objects in to abstract numbers.
An analog clock with constant rotation will show every moment in time uninterupted , a digital clock will never show the actual time.
Hello Everyone - I would enjoy hearing your comments about the video.
I have been looking for information like this for over 20 years online! You simplify it REALLY well! Thanks for doing this!!!
Glad you enjoyed it!
Time travel
You have been looking on UA-cam for 20 years?
This lecture is very interesting🤔
Thank you. Glad you found it interesting.
Great video. Keep up the good work!
Thank you for the comment. I've started now doing more work on the channel.
Amazing video! Really enjoyed! Do you have any reference, either for this or even further investigation? Like academic material or notes you based your reasoning on?
Thank you Nicola. I'm happy to hear you enjoyed the video. - As far as I know, there doesn't seem to be many good references, beyond looking at what we might refer to as a Pascal's Tetrahedron. There are a few references to hyper-tetrahedrons, but I took a different approach. Much of the material and ideas in the video are from my own work.
@@MikesFinancialEdge This video is beautiful, i'm sharing it with all my friends
I appreciate you sharing it with others! Thank you
Where does the fact at 9:50 come from? I understand that it does work, but why?
If you look at the faces of the tetrahedron it has to be the same as Pascal’s triangle by definition
hw d the exponents wrk? what is the pattern?
You just need 4 surface represent 4 term equation (a+b+c+d)^n, 3 surface represent 3 term equation(a+b+c)^n.
I think you have a mistake. If for Pascal's triangle you need the sum of 2 terms raised to a power n, for the tetrahedron you need the sum of 3 terms raised to a power n and so on. If I am in error, let me know.
Yes, we do use Pascal's triangle to expand two terms, but notice that we only use or need one row of the triangle when doing so. Take another look and let me know if you have questions.
I am a monkey
😀