• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

GCSE: Pythagorean Triples

Browse by

Currently browsing by:

Meet our team of inspirational teachers

find out about the team

Get help from 80+ teachers and hundreds of thousands of student written documents

  1. GCSE Maths questions

    • Develop your confidence and skills in GCSE Maths using our free interactive questions with teacher feedback to guide you at every stage.
    • Level: GCSE
    • Questions: 75
  2. Beyond Pythagoras

    1; 2(1)+1=3 If term number = 2; 2(2)+1=5 If term number = 3; 2(3)+1=7 This works for all Pythagorean triples that have an odd numbered SL. I have investigated another three Pythagorean triples and they are stated below. Serial No. Shortest side a Middle Side b Longest side c 1 3 4 5 2 5 12 13 3 7 24 25 4 9 40 41 5 11 60 61 6 13 84 85 I will now test the Pythagorean triples I have just found with the aid of Pythagoras theorem and a diagram.

    • Word count: 5018
  3. Investigate the area of triangle studies including the Pythagorean Theorem and in particular Pythagorean Triples, sets of numbers where the shortest side is an odd value and all three are positive whole integers.

    This means that the equation I want has nothing to do with 3 sides squared, and I can eliminate this from my list of sides to investigate. I will now try 2 sides squared. (Middle)� + Largest number = (smallest number)� = 122 + 13 = 52 = 144 + 13 = 25 = 157 = 25 This does not work and I know that neither will 132, because it is larger than 122. I have decided that there is also no point in squaring the largest and the smallest or the middle number and the largest number.

    • Word count: 3070
  4. Beyond Pythagoras.

    They are always consecutive numbers. I shall now investigate this. I will assume that the hypotenuse has length b + 1 where b is the length of the middle side. (c=b+1) b+1 a b Using Pythagoras: a? + b? = (b+1) ? Expanding this: a? + b? = b? + 2b+ 1 therefore a? = 2b +1 This means that a? must be odd because it equals 2b + 1. Since a? is odd this means that a must be odd also. (even x even = even)

    • Word count: 4266
  5. For this piece of work I am investigating Pythagoras. Pythagoras was a Greek mathematician.

    They are always consecutive numbers. I shall now investigate this. I will assume that the hypotenuse has length b + 1 where b is the length of the middle side. (c=b+1) b+1 a b Using Pythagoras: a� + b� = (b+1) � Expanding this: a� + b� = b� + 2b+ 1 therefore a� = 2b +1 This means that a� must be odd because it equals 2b + 1. Since a� is odd this means that a must be odd also. (even x even = even)

    • Word count: 4280
  6. Maths GCSE coursework: Beyond Pythagoras

    but this is a part of another pattern which is that the square of the shortest side is the same as the middle and longest sides added together, So... a� = b + c The theory works because: 12 +13 = 25 = 5� 5� = 12 + 13 This now allows to predict, odd starting, Pythagorean triples. It is correct! We have to, now, look at the smallest number. 3 5 7 9 11 13 2 2 2 2 2 1st difference The 1st difference is 2 so we must find the formula for the 'smallest number'.

    • Word count: 3537
  7. Beyond Pythagoras

    I also knew that c was probably one larger than b. I tried multiple triples until I found one that seemed to agree the theorem. I came up with 9, 40, 41. I proved that this was right: 92+402= 412 Because 92= 9x9= 81 402= 40x40= 1600 412= 41x41= 1681 81+1600= 1681 Next I needed to find the perimeter and area for this triple. I used the formula: Perimeter= a+b+c P= 9+40+41 P= 90 I found out the area using the formula: Area= (axb)?2 A= (9x40)?2 A=360?2 A=180 Next I updated my table: Length of Shortest Side (a)

    • Word count: 6029
  8. Maths Number Patterns Investigation

    4 +5 = 32 9 = 9 And... 24 + 25 = 72 49 = 49 It works with both of my other triangles. So... Middle number + Largest number = Smallest number2 If I now work backwards, I should be able to work out some other odd numbers. E.g. 92 = Middle number + Largest number 81 = Middle number + Largest number I know that there will be only a difference of one between the middle number and the largest number. So, the easiest way to get 2 numbers with only 1 between them is to divide 81 by 2 and then using the upper and lower bound of this number.

    • Word count: 3143
  9. Beyond Pythagoras

    Therefore, the first odd Pythagorean triple to satisfy these criteria is the 3,4,5 triple, and it is subsequently the first term of the odd triples sequence. The first sequence of triples that will be investigated are those with the first number (i.e. 3 of 3,4,5) as an odd number. I will refer to these triples as "odd triples" throughout the investigation for convenience. The second sequence of triples that will be investigated are those with the first number (i.e. 6 of 6,8,10, although this triple should not be counted as a "true" triple, as we shall see later)

    • Word count: 4016

Marked by a teacher

This document has been marked by one of our great teachers. You can read the full teachers notes when you download the document.

Peer reviewed

This document has been reviewed by one of our specialist student essay reviewing squad. Read the full review on the document page.

Peer reviewed

This document has been reviewed by one of our specialist student document reviewing squad. Read the full review under the document preview on this page.