# Contents of the March/April 1996 issue of Quantum

## Feature articles

### From the Edge of the Universe to Tartarus

#### by Albert Stasenko

The Greek poet Hesiod had a theory of how big the universe is: it would take an anvil nine days to fall from the heavens to the Earth, and another nine days for it to fall to the bottom of Tartarus (the underworld). How would a modern physicist go about checking the ancient poet’s numbers?

### Construction Program

#### by Alexander Kirillov

On March 31, 1795, the great mathematician Carl Friedrich Gauss constructed the regular 17-gon and was so impressed that he embarked on a mathematical career. Later Gauss proved the constructibility of regular n-gons for all numbers n that are “Fermat primes.” The author heads in the other direction and explains why regular polygons are constructible only for such values of n.

### From Mouse to Elephant

#### by Anatoly Mineyev

It’s amazing, in a way, that the shrew and the whale belong to the same biological family. In addition to sharing some obvious traits, all mammals have certain subtle characteristics in common. This article attempts to answer two simple questions: Why is the average diameter of a mammalian cell the value that it is? And why is it approximately the same for all mammals, even though their masses differ tremendously?

### How Many Divisors Does a Number Have?

#### by Boris Kotlyar

The Divisor Problem is one of the most interesting problems in number theory. Starting from his initial question (posed in the title), the author touches on the hyperbola, integer points on the plane, integration, and the natural logarithm, tying them together rather unexpectedly.

## Departments

### Kaleidoscope: The Long and Short of It

“Length” is one of the first geometric notions we encounter. It seems rather simple and straightforward—almost primitive. But investigations of length have led to some important mathematical concepts that are far from obvious and far-reaching in their consequences. (Click here to see an “ancient” instrument mentioned in this article (and in the Toy Store as well) but not depicted in the printed magazine.)

### Mathematical Surprises: The Golden Ratio in Baseball

#### by Dave Trautman

The famed Fibonacci sequence finds application in that favorite sport of statisticians and the statistically minded.

### Sticking Points: Surprises of Conversion

#### by I. Kushnir

Flip a theorem on its head, it’s still basically the same thing, right? Wrong. Sometimes it’s harder that it seems to prove the converse of a theorem.

### At the Blackboard I: A Gripping Story

#### by Alexey Chernoutsan

Six cases of static friction are presented, with an explanation of how to slide past them.

### In the Lab: Up the Down Incline

#### by Alexander Mitrofanov

The strange behavior of a double-cone roller—it goes up, when it “should” go down!

### Physics Contest: Sea Sounds

#### by Arthur Eisenkraft and Larry D. Kirkpatrick

Readers are invited to solve a problem from the XXVI International Physics Olympiad, held in Canberra, Australia, in July 1995.

### Math Investigations: The Orbit of Triangles

#### by George Berzsenyi

A short sequence of operations, repeated a thousand times or so, produces a “butterfly wing,” which readers are invited to investigate further.

#### by Ivan Depman and Naum Vilenkin

Learn some nifty number tricks that will confound your friends and won’t lose their charm even after you “let the cat out of the bag.”

### At the Blackboard II: So What’s the Point?

#### by Gary Haardeng-Pedersen

The author offers a way of replacing algebraic solutions to vector problems with geometric ones that may actually provide a better understanding of the physics involved.

### Toy Store: Nesting Puzzles (part 2)

This article picks up where part 1 left off (in the January/February issue), presenting two new puzzles and a method of solving them.

### Crisscross Science

Scientific crossword puzzle.