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Combinatorial Approach to Building a Dollar

The entire modern world relies on combinatorics. Combinatorics is the branch of mathematics studying finite or countable discrete structures (ESSENTIALLY, HOW MANY WAYS CAN YOU ORDER A SET OF OBJECTS USING A PARTICULAR SET OF RULES?).

Mathletes Week One: Building a Mathematical Team (Favorite Number, Counting Off, Helium Stick and Hoop)

We had a great kick-off to our first week of Mathletes for the 2016-2017 season. We started with introductions and name badges asking the children for their favorite number and why.

Architectural Floor Plans, Square Footage, and Designing Dream House

Last week, we explored another form of two dimensionality: square footage. Our exploration of fractals over the last two weeks seemed theoretical but next year we will discover the ubiquitous nature of fractals in our lives. This week’s lesson on architectural design focuses on a concept that is more concrete. 

Multiples of Composite Numbers Do Not Create Fractals on Pascal’s Triangle

Last week, the Mathletes proved that multiples of prime numbers create fractals (infinite complex self-similar patterns). In the process the children were exposed to the divisibility rules for prime numbers from 2, 3, 5, 7, 11, 13, and 17. The younger Mathletes focused on 2, 3, 5 and 7.

Pascal’s Triangle Prime Rows, Hexagon Sums, Fractal of Prime Multiples

One of the amazing properties of Pascal’s Triangle is that the prime rows (2,3,5,7,11,13,17,19,23,29…) are the ONLY rows of Pascal’s in which all numbers (except for the “1s”) are multiples of that prime number. For example, row 7 has 21, 35, and 42; row 11 has 55,165,330,and 462.