Category: Math

2021
Dec 11, 2021Math
Happy Numbers Visualization
In this article, we discuss happy numbers and a nice way to visualize them!
Jul 16, 2021Math
Dates in Arithmetic Progression
Can you find all dates that are in arithmetic progression?
Jan 27, 2021Math
Squares ending in xyxyxyxyxy
If a square number ( $a^2$ ) ends with xyxyxyxyxy, then xy should be one of 21, 29, 61, 69, 84, [Inspired by this Fermat’s Library LinkedIn post] To prove this, we first write $a = 5*10^9n+k$ Now, $a^2 = 25*10^{18}n^2 + 10^{10}nk + k^2$ Hence, the last 10 digits are determined by the last 10 digits of $k^2$ , $0 \leq k < 5*10^9$ . Although it is…
2020
Dec 14, 2020Math
Limiting Ratio of Tribonacci Numbers & Beyond
The Tribonacci series is 1, 1, 2, 4, 7, 13, 24, 44, … In this article, we find the limiting value of adjacent numbers.
Nov 21, 2020Math
Some Problems from Lilavati by Bhaskara II
A friend of mine posted this on LinkedIn. Quite interesting problems. It should be solvable at 8-10th grade levels. Solutions 1. Number of Apes Let A be the number of apes. It then follows: $A = \left(A/8\right)^2 + 12$ $\implies A^2 – 64A + 12.64 = 0$ $\implies A = (64 \pm \sqrt{64^2 – 48.64})/2$ $\implies A = (64 \pm 8.\sqrt{16})/2$ $\implies A = (64 \pm 32)/2$ $\implies A =$ 48 or 16 It is interesting to note there are two solutions to this problem…
Oct 22, 2020Math2 comments
An Angel Function!
I was playing with Desmos and I needed some function that would do some interesting things around a circle. I was tinkering, and accidentally found a function that draws something like an angel with wings stretched out :) $x = \left(2+2\ \sin t\right)\cos t$ , $y = \left(2+2\ \sin\ 3t\right)\sin\ t$ , $0 < t < 2\pi$ It looks like this. Does it look like an angel to you?…

Category: Math

2021

Dec 11, 2021Math

Happy Numbers Visualization

In this article, we discuss happy numbers and a nice way to visualize them!

Jul 16, 2021Math

Dates in Arithmetic Progression

Can you find all dates that are in arithmetic progression?

Jan 27, 2021Math

If a square number ( $a^2$ ) ends with xyxyxyxyxy, then xy should be one of 21, 29, 61, 69, 84, [Inspired by this Fermat’s Library LinkedIn post] To prove this, we first write $a = 5*10^9n+k$ Now, $a^2 = 25*10^{18}n^2 + 10^{10}nk + k^2$ Hence, the last 10 digits are determined by the last 10 digits of $k^2$ , $0 \leq k < 5*10^9$ . Although it is…

2020

Dec 14, 2020Math

Limiting Ratio of Tribonacci Numbers & Beyond

The Tribonacci series is 1, 1, 2, 4, 7, 13, 24, 44, … In this article, we find the limiting value of adjacent numbers.

Nov 21, 2020Math

Some Problems from Lilavati by Bhaskara II

A friend of mine posted this on LinkedIn. Quite interesting problems. It should be solvable at 8-10th grade levels. Solutions 1. Number of Apes Let A be the number of apes. It then follows: $A = \left(A/8\right)^2 + 12$ $\implies A^2 – 64A + 12.64 = 0$ $\implies A = (64 \pm \sqrt{64^2 – 48.64})/2$ $\implies A = (64 \pm 8.\sqrt{16})/2$ $\implies A = (64 \pm 32)/2$ $\implies A =$ 48 or 16 It is interesting to note there are two solutions to this problem…

Oct 22, 2020Math2 comments

An Angel Function!

I was playing with Desmos and I needed some function that would do some interesting things around a circle. I was tinkering, and accidentally found a function that draws something like an angel with wings stretched out :) $x = \left(2+2\ \sin t\right)\cos t$ , $y = \left(2+2\ \sin\ 3t\right)\sin\ t$ , $0 < t < 2\pi$ It looks like this. Does it look like an angel to you?…