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.