MATH DISCUSSION POST

Fibonacci Sequence. For this discussion you will post your own math problem

The Pythagorean Theorem is used to describe the relationship among the three sides in a right triangle. The relationship is generally written as a2 b2 = c2, where a and b are the short sides of the right triangle and c is the hypotenuse.

A Pythagorean triple is a set of three whole numbers {a, b, c} that satisfy a2 b2 = c2. For example, since 62 82 = (10)2, we say that {6, 8, 10} is a Pythagorean triple.

We can use the following steps to determine Pythagorean triples using any four consecutive Fibonacci terms or four consecutive Fibonacci-like terms.

Determine the product of 2 and the two inner Fibonacci numbers. This will

be a.

Determine the product of the two outer numbers. This is b.

Determine the sum of the squares of the inner two numbers. This will be c.

This process has produced the Pythagorean triple, {a, b, c}. You can verify by

checking to see if a2 b2 is equal to c2.

Here are two examples; Example 1 uses the Fibonacci terms 3, 5, 8 and 13. Example 2 uses the Fibonacci-like terms 1, 4, 5, 9

Determine the product of 2 and the two inner Fibonacci numbers.Example 1: the inner numbers are 5 and 8; the product of 2 and 5 and 8 is 80. This will be a.

Example 2: the inner numbers are 4 and 5; the product of 2 and 4 and 5 is 40. This will be a.

Determine the product of the two outer numbers.Example 1: 3 times 13 is 39. This is b.

Example 2: 1 times 9 is 9. This is b.

Determine the sum of the squares of the inner two numbers.Example 1: we have 52 82 = 25 64 = 89. This will be c.

Example 2: we have 42 52 = 16 25 = 41. This will be c.

This process has produced the Pythagorean triples. You can verify these!Example 1: {80, 39, 89}.

Example 2: {40, 9, 41}

For your initial post

Select four (4) consecutive Fibonacci terms or four (4) consecutive Fibonacci-like terms and use those four terms to create a Pythagorean triple by

following the four steps above. NOTE: You cannot use 3, 5, 8 and 13, or 1, 4, 5, 9.

Verify your results using the Pythagorean theorem.