python 2.7

16 = 21 Background: In number theory, a triangle number is an integer defined by the formula Inspiration for its name can be found in the figure above. The first few triangle numbers are 1, 3, 6, 10, 15, 21, 28. 36, and 4.5 In number theory, a square number is a square of an integer. For example, 0, 1, 4 and 9 are square numbers (020 12-1, 224, and 329) Every so often a triangular number may also be a square number. An integer that is both triangle and square is called a square triangle number. The first two square triangle numbers are 1 and 36 Your job: Write a program which prints the first 11 square triangle numbers. If we let Ni be the ith square triangle number, then your code is going to find , , N11 (we already know M = 1, N2-36). (HINT: Compute the triangle numbers recursively as discussed in class, otherwise your code will be too slow and may never finish!). Finally, numerically check the theoretical number theory result that 4 Verify this property by having your program output the raos the numerical value of V2), as well as the error: For full credit, your program must compute the triangular number according to the summation formula Eq. (4) and not some other (simplified) formula you find on the internet (the code must use a loop) Save your program as TriangleNumbers.py 16 = 21 Background: In number theory, a triangle number is an integer defined by the formula Inspiration for its name can be found in the figure above. The first few triangle numbers are 1, 3, 6, 10, 15, 21, 28. 36, and 4.5 In number theory, a square number is a square of an integer. For example, 0, 1, 4 and 9 are square numbers (020 12-1, 224, and 329) Every so often a triangular number may also be a square number. An integer that is both triangle and square is called a square triangle number. The first two square triangle numbers are 1 and 36 Your job: Write a program which prints the first 11 square triangle numbers. If we let Ni be the ith square triangle number, then your code is going to find , , N11 (we already know M = 1, N2-36). (HINT: Compute the triangle numbers recursively as discussed in class, otherwise your code will be too slow and may never finish!). Finally, numerically check the theoretical number theory result that 4 Verify this property by having your program output the raos the numerical value of V2), as well as the error: For full credit, your program must compute the triangular number according to the summation formula Eq. (4) and not some other (simplified) formula you find on the internet (the code must use a loop) Save your program as TriangleNumbers.py