MethodMath Math Questions and Answers

Another viral math meme:

People are arguing because:

• If you do $230 - 220 = 10$, then $10 \times 0.5 = 5$ ✓
• But PEMDAS says multiplication first: $220 \times 0.5 = 110$, then $230 - 110 = 120$.

So

I keep seeing videos about how pinecones, sunflowers, and even galaxies follow the Fibonacci sequence. Is this a real mathematical pattern in nature or just selective observation? What's the evolutionary

I understand that for arranging $n$ distinct objects in a line, there are $n!$ ways. But for a circle, the answer is $(n-1)!$. Why?

For example, with 4 people

I understand that factorial means multiplying down:

and

But then I see this:

and it feels wrong.

If there are zero numbers to multiply, why is the

Consider the Diophantine equation

where $p$ is a prime and we seek non-trivial integer solutions $(x,y,z) \in \mathbb{Z}^3 \setminus \{(0,0,0)\}$.

By a classical descent argument using the fact that $\mathbb{Q}(\sqrt{-3})$ has class

I am studying complex analysis and I need to understand the Cauchy-Goursat theorem. The theorem states:

If $f(z)$ is analytic in a simply connected domain $D$, then for any

I need to understand the logistic growth model:

where $r$ is the growth rate and $K$ is the carrying capacity.

I know this is a separable ODE, but I'd

The Banach-Steinhaus theorem (Uniform Boundedness Principle) states that for a family of bounded linear operators $\{T_\alpha\}_{\alpha \in A}$ from a Banach space $X$ to a normed space $Y$, pointwise boundedness implies