Top 10 Patterns in PASCAL'S TRIANGLE

Welcome to jensenmath, your go-to destination for captivating explorations in high school level mathematics! In this video, we delve into the mesmerizing realm of Pascal's Triangle, unraveling its top 10 most intriguing patterns that will leave you in awe.
From the enchanting symmetry of squares and cubes to the mystical allure of tetrahedral numbers, our journey through Pascal's Triangle is a testament to the beauty and elegance of mathematical phenomena. Witness the emergence of the Sierpinski triangle, uncover the hidden connection to the transcendental constants e and π, and prepare to be astounded by the depth of mathematical intricacies waiting to be discovered.
Each pattern is meticulously curated to captivate your mathematical curiosity, presented in an order that builds anticipation with every revelation. As we progress through the video, you'll find yourself drawn deeper into the enchanting tapestry of Pascal's Triangle, unlocking new insights and revelations along the way.
Here are the timestamps for each pattern:
0:00 - Pattern 10: Powers of 2
1:19 - Pattern 9: Powers of 11
3:44 - Pattern 8: Hockey Stick Pattern
4:40 - Pattern 7: Diagonals
7:08 - Pattern 6: Binomial Expansion
10:13 - Pattern 5: Squares
12:09 - Pattern 4: Fibonacci
13:20 - Pattern 3: Cubes
14:37 - Pattern 2: Sierpinski Triangle
16:16 - Pattern 1: e and π
But our journey doesn't end here! For those hungry for more mathematical exploration, be sure to visit jensenmath.ca, where you can access a treasure trove of free math resources to further deepen your understanding and appreciation of the mathematical world. Let's embark on this exhilarating journey together!

[@mr.pumpkinn]

The pascal triangle is perfect example for genius and simple

[@DefinitelyNotFelis.]

12:06 (talking about the 5th diagonal and the relevant numbers) - You substract the first number from the second number (5-1) and substract the difference (4) from the difference of the next two numbers (35-15), which is (20). You get the difference of (20-4), which is 16 - the square of (4).

[@thedeathofbirth0763]

Jensen, thank you for introducing us to the beauty of universality of patterns in math ! You rock !

[@arnavverma3434]

Next video idea: integrals that keep getting harder

[@zaqgamingstuff]

7:04 These equations for Pascal’s Triangle can also be used to estimate the area and shape of a 4D hyper-pyramid. The equation would probably be something like this: (n(n+1)(n+2)(n+3))/20

[@prod.gregupnext2958]

Im thinking about going back to college ,but do you have anything to help with teaching college entry math?

[@user-co6du3jh9f]

lol 2 years, comments: 13 hours