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

[lavliex]

I was watching the Diagonal Section and I noticed while you were talking about the tetrahedral numbers that if you add two adjacent numbers together, it equals the number underneath it.

[chramach]

AKS primality test is an algorithm used to determine whether a given number is prime or composite (not prime) which is based on Pascal's Triangle.🙂

[dococ]

there is a way to get Catalan numbers from the Triangle

[mosshead_vinsmoke]

Please do this to all general topics in Maths - trigo, geometry, PnC, Calc-1/2, Lin Alg, Disc Math....