Republic of Mathematics blog

Chicken soup for the mathematical soul

Posted by: Gary Ernest Davis on: March 27, 2011

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A few Twitter posts, following on the EdReach article “Khan Academy: Great Idea- With One Glaring Hole“, leads me this sunny New England Sunday morning to make a plea.

Jim Tanton

The plea is based on the outstanding series of videos posted by Dr. James Tanton on his site Thinking Mathematically!

Jim Tanton (@jamestanton on Twitter), a Princeton trained mathematician, does a superb job of teaching, explaining, teasing, stimulating, and generally engaging his audience in fun, deep mathematics.

This really is chicken soup for the mathematical soul.

My plea is for two other outstanding mathematics educators to put their thoughts in video form on the Web, so that we may be even better engaged and enlightened by their work.

These two highly trained, educated, and accomplished mathematics educators are Alexander Bogomolny and John Allen Paulos.

Alex Bogomolny

Alex Bogomolny (@CutTheKnotMath on Twitter) is the author, editor and curator of Cut The Knot, a website full of the most wonderful mathematical explanations, diversions, connections, and just plain interesting facts and ideas.

I would love to see Alex post videos in the form of Jim Tanton’s latest video series, where we see Jim giving his talks.

John Allen Paulos

John Allen Paulos (@JohnAllenPaulos on Twitter) is the author of many engaging and enlightening mathematics books. These are wonderful books that open people’s eyes to the need for numeracy in our modern world.

John is a wonderful expositor of mathematics and a real voice of conscience for basic quantitative thinking in matters of interest in society. I would love to see him post videos that did just that.

The reason I feel videos showing us these intelligent mathematicians thinking through issues is important is that living mathematicians are the embodiment of what the ancient field of mathematics is about.

They are people who can, by their presence, their thoughts, and their words, enlighten us to deeper mathematical thinking, encourage us to dig deeper, and more joyfully, and show us just how central and beautiful mathematical thinking is to human existence.

So how about it guys – can we expect to see you soon on the WWW internet screen?

Kinetic energy – when a vehicle stops suddenly, the energy has to go somewhere

Posted by: Gary Ernest Davis on: March 26, 2011

In: Uncategorized
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It’s an intuitive feeling that when we are driving a car, doubling our speed doubles our danger.

Sadly, this intuition is not correct.

Doubling our speed quadruples our danger.

The momentum of a car is the product of its weight $m$ (mass) and its speed $v$ (strictly speaking, the product of its mass and velocity).

Momentum doubles if the speed of a car doubles.

However, the kinetic energy – called the “living energy” by Leibniz – or the energy of motion, is $\frac{1}{2}mv^2$ .

That speed squared term in the kinetic energyÂ means that if the speed increases from $v$ to $2v$ – doubles in other words – the kinetic energy goes from $\frac{1}{2}mv^2$ to $\frac{1}{2}m(2v)^2= 4\times \frac{1}{2}mv^2$ .

That is, doubling a car’s speed leads to a quadrupling of its kinetic energy.

Because energy is conserved, if a car stops suddenly the kinetic energy – the energy of motion – has to go somewhere.

A lot of that energy will be transferred to energy of motion of the passengers – usually throwing them from the car and killing or seriously injuring them.

That square term in kinetic energy is one strong reason why speed can kill.