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

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."

Calculus Professor (via mathprofessorquotes)

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

Analysis professor (via mathprofessorquotes)

"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."

Anne Davenport, quoted in Paul Hoffman’s The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. (via deflect)

Draining bath tub swirls

spatialtopiary:

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 

image

p denotes pressure, g is acceleration due to gravity, and ρ is the uniform constant density (as this is a simple model). We assume that each particle traces a horizontal circle whose centre is on the fixed vertical axis z (see the diagram).

The speed image at a distance r from the axis is 

image

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

We are concerned with the region < 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

image

where c(z) is an arbitrary function and 

image

hence, c(z) = -ρgz + c0

where c0 is an arbitrary constant.

Hence, the pressure function can be expressed as

image

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 get

image

Hence, the depression in the free surface for r < a is 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 or c0 = p0, if we like.

image

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

curiosamathematica:

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.

curiosamathematica:

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&#8230;hello, everyone&#8230;

I checked, and sure enough, we&#8217;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 &#8212; submissions and full-time or part-time contributors are always welcome! [CJH]

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]