M3 Math Majors Matter ----------------------------------


Cartoon Corner

A Ponder ... (click picture to see)

A Mathematical Valentine

The Kiss Precise

By Fredrick Soddy (1936) (1921 Nobel Prize winner in Chemistry)

For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.

Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the center.
Though their intrigue left Euclid dumb

There's now no need for rule of thumb.
Since zero bend's a dead straight line
And concave bends have minus sign,

The sum of the squares of all four bends
Is half the square of their sum.

To spy out spherical affairs
An oscular surveyor
Might find the task laborious,
The sphere is much the gayer,
And now besides the pair of pairs
A fifth sphere in the kissing shares.
Yet, signs and zero as before,
For each to kiss the other four

The square of the sum of all five bends
Is thrice the sum of their squares.

The Kiss Precise (Generalized)

By Thorold Gosset (1937)

And let us not confine our cares
To simple circles, planes and spheres,
But rise to hyper flats and bends
Where kissing multiple appears.
In n-ic space the kissing pairs
Are hyperspheres, and Truth declares -
As n + 2 such osculate
Each with an n + 1 fold mate

The square of the sum of all the bends
Is n times the sum of their squares.
Top ten excuses for not doing homework:
  1. I accidentally divided by zero and my paper burst into flames.
  2. Isaac Newton's birthday.
  3. I could only get arbitrarily close to my textbook. I couldn't actually reach it.
  4. I have the proof, but there isn't room to write it in this margin.
  5. I was watching the World Series and got tied up trying to prove that it converged.
  6. I have a solar powered calculator and it was cloudy.
  7. I locked the paper in my trunk but a four-dimensional dog got in and ate it.
  8. I couldn't figure out whether i am the square of negative one or i is the square root of negative one.
  9. I took time out to snack on a doughnut and a cup of coffee. -- I spent the rest of the night trying to figure which one to dunk.
  10. I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.
A Conjecture ...
A conjecture both deep and profound
Is whether the circle is round;
In a paper by Erdös,
written in Kurdish,
A counterexample is found.

(Note: Erdös is pronounced "Air - dish") 

The good Christian...
... should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell. - St. Augustine
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