Mathematicians have been slicing open cones since the 4th Century BC. Here, we study one of these famous cross sections — the ellipse. Along the way, we’ll discover a beautiful proof from Germinal Dandelin of the 19th Century.

Slice a right circular cone at an angle to the horizontal. The cross-section forms an ellipse.

This one comes from Michael Penn, who in turn got it from a dead mathematician with a beard. You can check out Penn’s solution on his YouTube channel. The solution below is my own.

*Figure 1* shows a right triangle parachuting to the ground with a bedsheet.

Dear Readers,

Here is a neat application of Bayes’ Theorem. Imagine that a professor gives her students an exam. She wants to know how likely it is than any of them cheated. But she can’t just *ask* them. Can she even expect students to be report honestly on an anonymous survey? (Is it *really* anonymous? *Really?*)

I recently posted this on Reddit:

I am working on an article on Bayes Theorem and statistical significance, and I am asking for your help, dear Redditors! Here’s what I need you to do:1. Flip a coin.2. If the coin turns up…

The Binomial Theorem is commonly stated in a way that works well for positive integer exponents.

Last week, Dr. Peyam (of YouTube fame) published a video of a geometry problem he found on Instagram. The solution, he says, “uses a lot of beautiful geometry and even more beautiful calculus.” (It does indeed. Check it out.)

I am going to attack the same problem using methods that *predate* calculus — and even algebra. Here goes!

A parabola formed by the graph of ** y=x²** cradles a circle of radius

You have two circular washers. Each is made of the same material; each has the same thickness. The central holes of the two washers have different diameters.

On each washer, a straight line is drawn from one edge to the other, so it just touches the central hole. The two straight lines each have the same length *(Figure **1**)*.

The Secretary Problem is classic Decision Theory scenario. You must choose one of ** N** possible candidates. You have an objective way of ranking them. The proviso is that after you examine a candidate, you must either choose or reject that candidate. There is go going back for a second look.

For example, in ** Princess Alice and the 1,001 Suitors**, once Alice met a potential husband, she either decapitated him or married him.

`What strategy will maximize the probability of choosing the best candidate?`

Suppose you are at an automobile auction. Each of ** 19** cars will be displayed, one at a…

Here’s the challenge. You have three infinitely-sided dice. When you roll one of these dice, you get a Real Number between ** 0** and

Here’s the question. You roll the three dice. You square the outcome of each die.

`What are the odds that the `*sum of the three squares will be less than or equal to 1*?

These examples should clarify:

Here’s hoping you all had fun with last week’s Find the Zeros puzzle. As promised, here is my solution.

(Livestream recording on YouTube is ** here**.)

You may recall, we are looking for solutions to this function between ** 0** and

Your mission — should you choose to accept it — is to find the six roots between** 0** and

I am a maths/physics tutor in BC. You can find my stuff on YouTube: youtube.com/c/mathadam My Virtual Tip Jar: https://ko-fi.com/mathadam Thanks!