Math Magic is a web site devoted to
original mathematical recreations. If you
have a math puzzle, discovery, or observation,
please e-mail me about it. You can also send
answers to the problem of the month.
Math Magic Archive

Problem of the Month
(April 2014)

This month we explore approximations of the constants π and e using logarithms. We allow expressions to use the four arithmetic operations (× / + –) and the ln function. We measure the complexity of an expression as the number of integer digits used plus the number of logarithms used. Among all expressions using only one digit and logarithms with a given complexity, which one best approximates these constants? What if any digits can be used?

What if we are allowed to use square roots instead of logarithms? What if we are allowed to use decimal points instead? (I'm thinking that decimal points shouldn't count in the computation of complexity, since they cannot be used arbitrarily often.)


You can see all the best-known results here.

Submit your answers here.

Weekly Puzzle Sites: | Ken Duisenberg | NPR | Puzzability | The Griddle | Puzzle Picnic | Nick's |
Other Puzzle Sites: | MathPuzzle.com | IBM | Retrograde Analysis | Puzzle Palace | Terry Stickels |
Interactive Puzzle Sites: | Click Mazes | Puzzle Beast | Logic Mazes | Color Shift | Grid 1 | 2 | Boomshine |
Physics-Based Puzzle Sites: | Perfect Balance 1 | 2 | Assembler 1 | 2 | 3 | 4 | Splitter |
| Color Infection | Redstar Fall 1 | 2 | Fantastic Contraption |
Colleges with Puzzles: | Macalester | Missouri State | Purdue | Hamline |
Great Math Sites: | Geometry Junkyard | Math World | Mathematician Biographies |
| Integer Sequences | Inverse Calculator | Geometric Dissections |
Recreational Math Sites: | Mike Keith | Harvey Heinz | Primes | GIMPS |
| Polyforms | World of Numbers | Soup Kitchen |


Home | Math Magic | Packing Center | Puzzle Palace | Published Puzzles | Puzzle Collection
Friedman Numbers | What's Special About This Number? | Periodic Table of Mathematicians
Stetson University | Math Department | Teaching | Vita | Undergraduate Research | Ambigrams
Florida Mini-Golf | Movies | Places I've Been | Places I've Been E-mailed From | E-mail Me
Pictures of Me | My Math Geneology | Top Ten Lists | Mathematical Horoscope | Math Humor