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in this video, we are going to learn about 12 unknown facts about the pascal's triangle.
So don't forget to watch till the end 🤗🤗
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About a year ago, while I was recuperating from a heart attack in a nursing facility, I got very bored with TV so I got a friend of mine to bring me a calculator so I could play with numbers, which I sometimes enjoy doing.
I decided to see if I could find a method of generating the sequences of numbers in the diagonals of Pascal's Triangle, not expecting to succeed. But I actually did succeed!
I'll show y'all what I found:
The first two diagonals are pretty trivial, so I'll begin with the third diagonal.
1×3/1=3
3×4/2=6
6×5/3=10
10×6/4=15
15×7/5=21
21×8/6=28
28×9/7=36
36×10/8=45
45×11/9=55
55×12/10=66
Etc.
1×4/1=4
4×5/2=10
10×6/3=20
20×7/4=35
35×8/5=56
56×9/6=84
84×10/7=120
120×11/8=165
165×12/9=220
220×13/10=286
Etc.
1×5/1=5
5×6/2=15
15×7/3=35
35×8/4=70
70×9/5=126
126×10/6=330
330×11/7=495
495×12/8=715
715×13/9=1001
Etc.
1×6/1=6
6×7/2=21
21×8/3=56
56×9/4=126
126×10/5=252
252×11/6=462
462×12/7=792
792×13/8=1287
1287×14/9=2002
Etc.
That should be enough to give y'all the basic idea. This will work for any of the other diagonals as well!
Enjoy!
Which one is your favourite 😍😉
Comment below 🤗🤗
the one which equals to e when n -> infinity, so special
e and pi ones
Great video, Ujjwal! Happy to see you included e. For anyone interested, here are the papers that announced the discovery:
H. J. Brothers, Finding e in Pascal’s triangle, Mathematics Magazine, Vol. 85, No. 1, 2012; page 51.
H. J. Brothers, Pascal's triangle: The hidden stor-e, The Mathematical Gazette, Vol. 96, No. 535, 2012; pages 145-148.
Thank you for this information 😊
Excellent Mathocube! Keep up the good work 👍
Nice👍👍
Excellent👍👍
Excellent 👍👌
12 is Highly Composite Number
Bro take this another level🎉
Excellent 👌👍💯🆗😃
Show man mandou super bem
Sum of diagonal numbers equal to near off number.
Thanks for sharing and effort of the informative video. May I ask which computer program did you used for visual representations?
it's probably Manim.
Amazing
Awesome 👍👍
Nice 👏👏
Try these. Given 11^n relationship. 101^n. (73^n)(137^n). (7^n)(11^n)(13^n).
Great suggestion!
Fibonacci 1/89 and the Powers of 11
1/89
0.01123595505617977528089887
1/989
0.001011122345803842264914054
1/9989
0.0001001101211332465712283511
1/99989
0.0000100011001210133114642
1/999989
0.000001000011000121001331014641
1/9999989
0.0000001000001100001210001331001464101610511
@@Mathocube
🎉🎖
The alternating adding and subtracting of reciprocals of the 3rd row of pascals triangle does not equal pi - 2. pi - 2 is equal to about 1.14159265... but the reciprocals of the 3rd row of pascals tringles, comprising of the triangular numbers, when alternatingly added and subtracted in fact add up to 0.772588... or the ln(16) - 2, not pi - 2.
Points on a circle is astounding
How about 3 digit number
🎉
Pascal triangle know but more today know
#12
1+3+6+10=20, not 1+6+10=20…..
Its not easy