(02/05/96) ************************************* MathMagic Cycle 20: Level 7-9 Regular ************************************* Primitive* Pythagorean Triplets a b c Based on the Pythagorean theorem (a^2+b^2=c^2) the ----- ----- ----- table at the left has been developed. 3 4 5 5 12 13 Working with your team and NTPs, try to come up 7 24 25 with at least EIGHT questions, observations or 8 15 17 hypothesis based on the data, that perhaps would 9 40 41 be valid if more elements were added to the table. 12 35 37 Example: All c's seem to fit a 4n+1 pattern. (*) When a, b and c are relatively prime (they have no factor in common other than 1) the Pythagorean Triplets are said to be Primitive ************************************** MathMagic Cycle 20: Level 7-9 Advanced ************************************** Pascal's Triangle is an expansion that has many 1 mathematical applications. 1 1 1 2 1 Work with your team and your NTP to "present" three 1 3 3 1 of them. Your research and exchanges should lead you 1 4 6 4 1 to discover at least one use that may be labeled 1 5 10 10 5 1 bizarre (or at least "really weird") ============================ Good luck MrH