Funny Math Shirt by Fraggles & Friggles at http://etsy.me/1fG9x7n

An explanation of the Monty Hall Problem, by James Grime.

### "Pictures and intuition are an excellent way to convince people that false things are true."

### "Eventually" basically means "finitely much foolin’ around with arbitrary values."

### "There was a time at Trinity College, in the 1930s I believe, when Erdős and my husband, Harold, sat thinking in a public place for more than an hour without uttering a single word. Then Harold broke the long silence, by saying, “It is not nought. It is one.” Then all was relief and joy. Everyone around them thought they were mad. Of course, they were."

*The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth.*(via deflect)

### Draining bath tub swirls

So, y’know that little dimple found at the plug holes of draining baths and sinks, in the top of hurricanes and in coffee if swirled in a circular function? Well I sure do. And I was wondering what form it would take. So I worked it out.

Using the Euler Equations for an ideal, incompressible flow in cylindrical polar coordinates, at position

(r, θ, z), for a stationary flow which is independent of θ, we have

pdenotes pressure,gis acceleration due to gravity, andρis the uniform constant density (as this is asimplemodel). We assume that each particle traces a horizontal circle whose centre is on the fixed vertical axisz(see the diagram).The speed at a distance

rfrom the axis is(I looked this up in a set of fluid mechanics notes dealing with a similar problem)

We are concerned with the region

0 < r < a, i.e. the dip in the surface of our fluid.If we look back at the first couple of equations, we can see that

where

c(z) is an arbitrary function andhence,

c(z) = -ρgz + c0where

c0 is an arbitrary constant.Hence, the pressure function can be expressed as

At the free surface of the water, the pressure is constant atmospheric pressure

p0, if we substitute this into the pressure function and rearrange, we getHence, the depression in the free surface for

r<ais a parabolic surface of revolution.Note that the pressure is only ever globally defined up to an additive constant so we can take

c0 = 0 orc0 =p0, if we like.Much of this is based on the introductory fluid mechanics course delivered by Simon J A Malham at Heriot Watt University in the spring of 2013

The Google trend for the search query “

quadratic formula”.It repeats in the same pattern every year. Down in summer, up in September, down again in December and up again in spring time before going down again in the summer. And so it goes on forever.

Woke up to this email this morning…hello, everyone…

I checked, and sure enough, we’ve gotten almost 80 followers in the past 24 hours. (Wow!) On behalf of both Kailyn and myself, welcome to Mathematica! We hope to continue to deliver you high-quality math content, and just a reminder — submissions and full-time or part-time contributors are always welcome! [CJH]