Abhishek Verma 💻

Yes, x = a + b ✅ A simple visual proof would be to fold it along the lines AE and AF, then points D & B meet on EF. Mathematically, it can be easily proven by moving △ABE as shown below. Then △EAF and △E'AF are congruent. Hence proving: x = a + b

The complexity of this problem is surely being underestimated. For those interested in the answer, its possible but numbers are huge.

With 4 colors

An interesting way to check if the given alphabet is vowel using bit manipulation. Have a look if you understand how it works !

Also, I discovered a fascinating phenomenon for the current years (2022-2025), they're Harshad years. To begin, Harshad number is a number divisible by sum of its digits. E.g. 2023 is divisible by 2+0+2+3 ie 7. But this phenomenon (2+ consecutive Harshad years) is so rare that it last happened 1000+ years back for 1014-1017. And will next happen after 1000+ years in 3030-3033.

Trigonometrically, tangent of 2025° is 1. Obviously, happens 180 years apart. And since, 2025 = 27² + 36² Hence, 2025 can be represented as hypotenuse of a right triangle with integral sides. Last such year was 1681 ( = 9² + 40²), Next such year will be 2809 ( = 28² + 45²).

2025 is a centered octagonal number. Such numbers are represent an octagon with a dot in the center with surrounding dots in successive octagonal layers. Last such year was 1849, Next such year will be 2209.

As per Nicomachus' theorem: 1³ + 2³ + ... + n³ = (1 + 2 + ... + n)² Hence, the previous fact can also be stated as 2025 being square of a triangular number. 2025 = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)²

Happy New Year, 2025 ! 🥳🎉✨ May this year bring you joy, prosperity and everything you wish for ! Numerically, year 2025 holds rare gems which won't occur for decades and centuries. Let's explore 🧵👇

Exterior angle of triangle = sum of opposite interior angles Hence, the other two angles in triangle including A are "C+D" and "B+E" as shown below. ⇒ A + B + C + D + E = 180° ✅