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Mathematical Mazes for the Mind

The course is designed to cover a variety of topics with an emphasis on an appreciation of the elegant nature of mathematics by exploring unusual, yet enriching mathematical topics.

Instructor: Akehiko Takahashi
BS in Mathematics, MA in Political Science
Retired from Wentzville School District
Email: edokko@hotmail.com or taisomaster@yahoo.com

Rational for inclusion in a program for the gifted students:
Gifted students should be exposed to more challenging topics in mathematics not normally covered in classroom.

Major topics covered

GRAPH AND DATA REPRESENTATION
Histogram, dotplots, stem-&-leaf, Pareto Chart, Scatter
diagrams, Venn diagrams, Shlegel diagram, Argand, isobar,
polar graph, 3D Bar Graphs, Box-and-whisker, UPC code, Bell
curve, Wire Frame, etc.

TRIANGLES
Golden, Reuleaux, Penrose, Heronian, Morley's, Pedal, Medial,
Yff, Homothetic, Orthic, Kaniza, Cevian, and Work Triangle,
Trefoil, Triangular numbers, Viviani Theorem, Enriching 3-4-5
right triangle by adding other important items (1-2-3-4-5-6)

AVERAGES
Arithmetic, geometric, subcontrary (harmonic) semi-harmonic, quadratic mean, Heronian, golden mean, weighted mean, root mean square

NUMBERS
Mersenne, Fermat, primorial prime, Sophie Germain prime, factorial prime, Gaussian prime, Boolean Abundant and Deficient, Base numbers, complex, Quarternion, figurate, Lucky numbers Ludolphian, Niven, Perfect, Euler number, Fobonacci, RSA encryption and patents on prime numbers, Sub factorial.

SEQUENCE
Arithmetic, Geometric, Harmonic, Fibonacci, Lucky, Conway sequence, Farey sequence, Doublets (invented by Lewis Carroll), RATS sequence, Ulam sequence, Aronson's and various other sequences.

Prerequisite: ability to think well and comprehend new topics

Learning Objectives
Learn mathematical topics not usually found in normal high school curriculum and be able to use them effectively.

Primary sources: Dictionary of Curious and Interesting Numbers
By David Wells
Intriguing Mathematical Problems by Jacoby

Supplementary source materials:
Curious and Interesting Geometry by Wells
Ingenious Mathematical Problems and method by Graham
Intriguing Mathematical Mysteries by Joseph Konhauser
Joy of Mathematics by Pappas
Puzzles, Mathematical Diversions, and Brainteasers by Brecher
Curious Problems and Puzzles by Dudney
Encyclopedia of Mathematics by Weisstein

Computing and the Internet
Use Internet for research purposes

Typical classroom strategies:
Students will work together to answer questions presented in classroom. Students will encounter daily some challenging Mensa or AHSME types of questions and they must work together to come up with reasonable solutions. They will discuss methods for getting answers and look for better or simpler solutions, if any.