Intereting Posts

How to evaluate $\int_{0}^1 {\cos(tx)\over \sqrt{1+x^2}}dx$?
Calculate the integral $\int_{0}^{2\pi}\frac{1}{a^{2}\cos^2t+b^{2}\sin^{2}t}dt$, by deformation theorem.
Mathematical Telescoping
No primes in this sequence
Number $N>6$, such that $N-1$ and $N+1$ are primes and $N$ divides the sum of its divisors
Does an infinite random sequence contain all finite sequences?
Is every $F_{\sigma\delta}$-set a set of points of convergence of a sequence of continuous functions?
Derivative of convolution
Dimension of a Two-Scale Cantor Set
Prime $p$ with $p^2+8$ prime
Where can I find the paper by Shafarevich on the result of the realization of solvable groups as Galois groups over $\mathbb{Q}$?
Concept behind the limit to infinity?
Proving $\prod_k \sin \pi k / n = n / 2^{n-1}$
Do values attached to integers have implicit parentheses?
The direct image of an ideal need not be an ideal

Walking with my son at 3:14pm the other day, I mentioned to him, “Hey, it’s Pi Time”. My son knows 35 digits of $\pi$ (don’t ask), and knows that it’s transcendental. He replied, “is it **exactly** $\pi$ time?”

This led to a discussion about whether there is ever a time each afternoon that is exactly $\pi$, meaning 3:14:15.926535…

This feels like some kind of Zeno’s Paradox. I told him that (assuming time is continuous) it had to be $\pi$ time at some point between 3:14:00 and 3:15:00, but the length of that moment was 0. However, this discussion left him confused.

- Simple Proof of the Euler Identity $\exp{i\theta}=\cos{\theta}+i\sin{\theta}$
- How to justify small angle approximation for cosine
- Motivating implications of the axiom of choice?
- Learning Combinatorial Species.
- What are some surprising appearances of $e$?
- How do I explain 2 to the power of zero equals 1 to a child

Can anyone suggest a good way to explain this to a child?

- How do you calculate the decimal expansion of an irrational number?
- Very *mathematical* general physics book
- Irrational numbers to the power of other irrational numbers: A beautiful proof question
- What is the importance of Calculus in today's Mathematics?
- Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
- Quickest way to understand Kruskal's Tree Theorem
- How do you remember theorems?
- Is $\frac{1}{11}+\frac{1}{111}+\frac{1}{1111}+\cdots$ an irrational number?
- Prove that the exponential function is differentiable
- Why is negative times negative = positive?

Pi time is not like a concrete slab on the sidewalk that you can stand on; it’s not even like the crack between the slabs, which have a width. It is like the line precisely down the middle of that crack. When you’re walking on the sidewalk, you cross right over it without stopping on it.

And so is every other precise time: like exactly noon or midnight.

Of course, the analogy fails a little bit because when you stop on the sidewalk, you cover a whole range of positions. As far as we can tell in everyday life, that’s not true of time… not that we can stop in time, anyway…

That is how I would explain it to a non-mathematician.

- Why are the periods of these permutations often 1560?
- Why can't we construct a square with area equal to a given equilateral triangle?
- Why the set of outcomes generated by a fixed strategy of one player in Gale-Stewart game is a perfect set?
- Can one construct a non-measurable set without Axiom of choice?
- proof Intermediate Value Theorem
- Why is there no “remainder” in multiplication
- About the Order of Groups
- finding examples for a non negative and continuous function for which the infinite integral is finite but the limit at infinity doesn't exist
- Second-order non-linear ODE
- Sum equals integral
- Where do summation formulas come from?
- Carmichael number factoring
- $\forall A\subset \mathbb{N}$ the sum of the reciprocals of $A$ diverges iff $A$ is $(\tau, \mathbb{N})$-dense
- How to evaluate $\lim_{n\to\infty}\sqrt{\frac{1\cdot3\cdot5\cdot\ldots\cdot(2n-1)}{2\cdot4\cdot6\cdot\ldots\cdot2n}}$
- Why does polynomial factorization generalize to matrices