Mike Johnson

I learned a little about Laplace transforms in differential equations, and now Fourier transforms are showing up in signals and PDEs.

They look similar because both are integrals that transform a function:

I always struggle to calculate tips at restaurants. Whats the fastest mental math trick?

For 15% tip:

1. Calculate 10% (move decimal left one place)
2. Take half of that for 5%
3. Add them together

Since the meme showed $5! = 120$, I started thinking about factorials. $0! = 1$ $1! = 1$ $2! = 2$ $3! = 6$ $4! = 24$ $5! = 120$ $6! = 720$ $7! = 5040$ $8! = 40320$ $9! = 362880$ $10! = 3628800$

The Collatz conjecture: Start with any positive integer $n$. If $n$ is even, divide by 2: $n \to n/2$. If $n$ is odd, multiply by 3 and add 1: $n \to 3n + 1$.

Ive been trying to find a pattern in prime numbers. The primes up to 100: $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97$

The internet is arguing about this again: How many squares are in a chessboard? A chessboard is $8 \times 8$. Most people say 64 (the $1 \times 1$ squares). But theres also: - $2 \times 2$ squares: $7 \times 7 = 49$ - $3 \times 3$ squares: $6 \times 6 = 36$ - ... - $8 \times 8$ squares: $1 \times 1 = 1$

I asked ChatGPT to integrate: $$\int \frac{\sin^3 x}{\cos^2 x} \, dx$$

Ive read like 10 explanations and I STILL dont get why you should switch.

The setup: 3 doors, 1 car, 2 goats. You pick a door. Monty (who knows where the car is) opens a different door revealing a goat. Now you can switch to the remaining door.

This trick is all over Instagram: To multiply $23 \times 47$: $$20 \times 40 = 800$$ $$20 \times 7 = 140$$ $$3 \times 40 = 120$$ $$3 \times 7 = 21$$ Total: $800 + 140 + 120 + 21 = 1081$

In school they told us "you cant divide by zero" but they never explained WHY.

Like if you divide a number by a really small number you get a really big number right?

I saw the Numberphile video and now my whole class is confused. $$1 + 2 + 3 + 4 + \cdots = -\frac{1}{12}$$

I keep seeing this on TikTok and Twitter and everyone argues in the comments. Please settle this once and for all: $$8 \div 2(2+2) = ?$$