Arithmetic education for children: When are triangles squares? ● Rabbi Yitzchak Ginsburgh

[Suivlys]

Hey, but 1681 is also a square, square 41.

so the next ST number 1413721 is also both a square (1189) and the triangle of a square (41)

[Suivlys]

There is another strange thing

49 is square 7

So 1225 is both a square (35) and the triangle of a square (7)

I cannot figure out so quick the next number that is both a square and the triangle of a square.

7 and 35 sure are signicant Torah-numbers.

The account of the seventh day (Genesis 2:1-3) is written with 35 words.

[justkimmusic]

Excellent lecture, lucky kids!

[Suivlys]

= T 1681 = S 1189

[Suivlys]

K5 = 34 * 41616 - 1225 + 2 = 1413721

[Suivlys]

The nth Square Triangular number Kn can easily be obtained from the recursive formula

Kn = 34 * Kn-1 - Kn-2 + 2.

So knowing the first two ST numbers i.e. K1 = 1 and K2 = 36 , all other successive Square Triangular numbers can be obtained , e.g.

K3 = 34 * K2 - K1 + 2 = 34 * 36 -1 + 2 = 1225

K4 = 34 * K3 - K2 + 2 = 34 * 1225 - 36 + 2 = 41616

K5 = 34 * K4 - K3 + 2 = 34 * 41616 - 1225 = 1413721

[jeffaholman]

49 x 50 / 2 = 1225 (triangle of 49)

35 x 35 = 1225 (square of 35)

[innerorg]

Something to know about the Rav and his teachings. In the 15 years I have heard him speak -- thousands of hours worth of speaking -- and have worked on his books, I have never seen him make s single math error. Everything he says is very accurate, he does not fudge.

[innerorg]

No. the triangle of 49 is 1225. The whole point here is that there are numbers that are both triangular and square. 1225 is both the triangle of 49 and the square of 35. You can also see the article on our website titled When two triangles make a square.

[ruffyatutube]

i.e., the triangle of Sefirat HaOmer is actually "triangle 50"!



[ruffyatutube]

The Sfirat HaOmer triangle , triangle 49 = 1176 !!!

I suppose the rabbi wants to say the triangle of 50, not 49!!

[chaimke7]

who did the homework

[Tzalaf5731]

OUTSTANDING! What A Powerful Shiur!

Thank You Rabbi Ginsburgh.

[jeffaholman]

NICE