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Pascal’s Triangle Patterns and Combinations

Now that the children have discovered the process of building the most famous array of numbers in Pascal’s Triangle, we began to discover its many patterns. 

Pascals Triangle: Diagonals of "1s", "2s", "counting", and "prime" numbers; 12, 20, and 29 Rows

Pascal’s Triangle is named after the French mathematician and philosopher Blaise Pascal (1623-1662). It is a triangular array of counting numbers. “1s” are placed along the diagonals and each other cell is the sum of the two cells above it. The largest number on the 12th row of Pascal’s Triangle is 924. The largest number on the 20th row of Pascal’s Triangle is 184,756.

Prime Pyramid

A prime number is a whole number that has exactly two factors--itself and 1. Last week, we introduced a new discovery regarding the lack of randomness of prime numbers. I have developed a challenge called a prime pyramid where each row begins with 1 and ends with the number of that row. So, row 2 begins with a 1 and ends with a 2, row 3 begins with a 1 and ends with a 3, and so on.

Logic-Based Problem Solving Math Competition Spring 2016

Game day is here. The Spring 2016 Math Competition was handed to your children during class this week. I asked them not to open the test until they can commit to spending 45 uninterrupted minutes. They should be sequestered in a quiet room with only a few pencils and good light. Siblings should be asked to be in a separate part of the house and not above the room in which the Mathlete is taking the test. 

Prime Numbers Are Not Random Proves Stanford Mathematicians

On March 11, 2016 mathematicians from Stanford University proved that prime numbers do not behave randomly as previously thought.