Nearly a decade ago, a user named a_hardin posted to the Mathematics Stack Exchange: Is this Batman Equation for Real? The question gained 466 upvotes before moderators closed it. The accepted solution, by ShreevatsR received 1085 upvotes for its magnificent dissection of the equation.
I have often wondered if I, myself, am capable of such mathematical acrobatics. So I finally tried. Here are my results.
My image consists mostly of parabolas and a few quartics. I broke the image down into eleven strokes. …
My student pondered the diagram before her. The vectors stared back at her from the whiteboard, daring her to dissect them.
“Do you want to make this easier?” I said, tilting the whiteboard to a 45-degree angle.
“You can do that?”
“Sure. Why not?”
I’m a believer in encouraging students to discover unconventional approaches to problems. Sometimes they might discover a simpler approach. Often they won’t. Most of the time, the experience will enrich understanding of some principle.
Consider this integral:
After the publication of What If Your Cat Became A Black Hole?, a lot* of people signed up for the MathAdam newsletter. It got me wondering:
What have all these folks gotten themselves into? (Yes. Gotten is a word. I checked.)
The simplest thing to do is to ask.
So, I’m asking.
What would you like to see from MathAdam? I have an itty bitty form for you to submit your responses. All respondants will receive warm feelings.**
Thanks much! And I look forward to sending more mathy/fizzixy stuff your way.
*Approximate figure only.
** Warm feelings have no cash value and are non-transferable. Void where prohibited by law and/or divine fiat.
You may already know the famous (infamous?) Blue-Eyed Islander Puzzle. Here’s my version.
99 perfect logicians are stranded on a remote island. As perfect logicians, each is able to immediately determine the logical outcome of any statement. These perfect logicians all have blue eyes. Each Islander is able to observe all the others. However, they are all unable to communicate with one another. Furthermore, each is (somehow) unable to observe his/her own eye colour.As a result of these circumstances, each logician knows the following to be true:At least 98 people here have blue eyes.Each day at noon…
It is very rare these days for a domestic feline to spontaneously form a black hole. However, it’s best to be prepared for such an unlikely event. Here is what would happen.
A black hole is an object of such gravitational profundity, even light cannot escape its clutches.
Imagine a flea leaping from your cat. Assume that your cat has a mass of 1 kilogram. And is perfectly spherical, with a radius of 0.1 metres. We’ll treat as negligible the mass of the Earth, air resistance and the laws of probability.
King Bob and his loyals subjects have been planning King Bob Day for years. Finally the day is upon us! The Royal Vintner has set aside 1,000 bottles of the finest aged wine in honour of the occasion.
Tragedy and heartbreak! King Bob learns through his Royal Intelligence Agency that his nemesis, Duke Ralph, has had exactly one of the bottles poisoned. Not one, but ten traitors have been bought by Duke Ralph to sabotage the festivities.
King Bob rounds up the ten traitors and has them thrown into the dungeon. He then personally questions them.
“Where is the…
Canadian mathematician Ivan Niven has provided us with a proof that π is irrational. This proof requires knowledge of only the most elementary calculus. The difficult part is following the trail of the argument.
His paper, enticingly titled A Simple Proof That π Is Irrational is just one page long. However, as is often the case, his compact argument leaves the reader to fill in many details.
I will try to unpackage that argument now.
This is a proof by contradiction. We begin with the assumption that π is rational. …
We know that e and π are both irrational numbers. Neither can be written as a ratio between two integers.