'Math Ia Type 2 Stellar Numbers.\r'

'Math SL Investigation fount 2 Stellar Numbers This is an investigation about stellar crooks, it involves geometric shapes which devise special anatomy patterns. The simplest of these is that of the squ ar rime (1, 4, 9, 16, 25 etc…) The diagram beneath shows the stellar triangular numbers until the 6th triangle. The succeeding(prenominal) three numbers after T5 would be: 21, 28, and 36. A general statement for nth triangular numbers in hurt of n is: The 6-stellar star, where there are 6 vertices, has its first four shapes shown below:The number of dots until stage S6: 1, 13, 37, 73, 121, 181 Number of dots at stage 7: 253 Expression for number of dots at stage 7: Since the general trend is adding the next multiple of 12 (12, 24, 36, 48 etc…) for each of the stars, so for S2 it would be 1+12=13, and for S3 it would be 13+24=37 popular statement for 6-stellar star number at stage Sn in damage of n: For P=9: Since S1 must fitted 1 then we lavatory prove this for mula by showing that:So the first six terms are: 1, 19, 55, 109, 181, 271 Therefore the equating for the 9-Stellar star at For P=5: Since S1 must equal 1 then we can prove this formula by showing that: So the first six terms are: 1, 11, 31, 61, 101, 151 So the expression for 5-Stellar at General Statement for P-Stellar numbers at stage Sn in terms of P and = For P-Stellar number equals 10: For P-Stellar number equals 20: The General Statement works for all number fro 1 to positive infinity.The equivalence was arrived at since the sum of arithmetic series can be found using , since the rest is forever 2P then we can replace 2P with d, and since u1 is always equal to 1, we can replace it with 1 every time. The at the end of the equation serves the purpose of making the difference between the numbers in the series constant. This form of the equation will allow for only wiz variable to change, which will be . One of the things the educatee realized while solving this investigation was that the stand by term is always equal to , but the derived equation which is also works.\r\n'