... = 37 666 = 37 999 = 37 777 = 37 9 12 18 27 21 It seems that when all the 3 digits are the same number the answer to the problem is 37. Can I use Algebra to explain this? aaa=100a+10a+a =111a = 37 ...

... 24 = 576 25² = 25 x 25 = 625 and so 7² + 24² = 49 + 576 = 625 = 25² For the set of numbers 3, 4 and 5: Perimeter = 3 + 4 + 5 = 12 Area = 1/2 ...

... (c; the longest), the perimeter (P) and area (A) of a right-angled triangle. Please note: Throughout this investigation, the sum on the bottom line is the final answer to each set of sums. For example: y=2+2 y=4 In this example, the bottom line (y=4) ...

... (1) squared by two is not a whole number print a zero, but if it is a whole number print the number. The integer of a number is the bit after the point. I took the square root because only a certain ...

... results for perimeter and area into the table below. Length of Shortest Side (a) Length of Middle Side (b) Length of Longest Side (c) Perimeter (P) Area (A) 3 4 5 12 6 5 12 13 30 30 7 24 25 56 84 3. Before investigating patterns I tried to find the Pythagorean triple for a shortest side of 9 to increase ...

... to see if these triangles fit into pythagoras' triangle theorem: a) 5, 12, 13 b) 7, 24, 25 Both fit into the pattern. The numbers, 3, 4, 5 could be used to make a right angled triangle as shown below: ...

... I will try and work out patterns and formulas to help me work out the value of a, b and c and the perimeter and area of the triangles. (n) (a) (b) (c) (p) (Area) 1 3 4 5 12 6 2 5 12 13 30 30 3 7 24 25 56 84 4 9 40 41 90 180 5 11 60 61 132 330 6 13 84 85 182 546 7 15 112 113 240 840 8 17 144 145 306 1224 Formulas: The formula for a is: N a 1 3 = 1 ×2 + ...

... Pythagorean Triples Table of first 10 odd triples n a b c Perimeter Area 1 3 4 5 12 6 2 5 12 13 30 30 3 7 24 25 56 84 4 9 40 41 90 180 5 11 ...

... (3,4,5), (5,12,13) and (7,24,25) to find other triples. Then I will put my results in a table and look for a pattern that will occur. I will then try and predict the next results in the table and prove it. ...

... 576 = 625 625 = 625 (3, 4, 5), (5, 12, 13) and (7, 24, 25) are called Pythagorean triples because they satisfy the condition, (Shortest side)2 + (Middle side)2 = (Longest Side)2 We know from the Pythagorean triples the shortest side is ...

... a few patterns emerging. Here they are: i. The shortest side is always an odd number. ii. The medium side is always an even number. iii. The medium side plus one equals to the Longest side. iv. The Longest side is always odd. To ...

... a few patterns emerging. Here they are: i. The shortest side is always an odd number. ii. The medium side is always an even number. iii. The medium side plus one equals to the Longest side. iv. The Longest side is always odd. To ...

... 576 = 625 625 = 625 (3, 4, 5), (5, 12, 13) and (7, 24, 25) are called Pythagorean triples because they satisfy the condition, (Shortest side)2 + (Middle side)2 = (Longest Side)2 We know from the Pythagorean triples the shortest side is ...

... always even numbers. I can immediately see the formula to derive the shortest side length from the term number. The term multiplied by two add one equals the shortest side length. Let Shortest Side Length = SL Term = T Term Number = ...

... 4 = 16 52 = 5 x 5 = 25 and so 32 + 42 = 9 + 16 = 25 = 52 The numbers 5, 12, 13 and 7, 24, 25 also work for this theorem and satisfy the condition. ...

... 3, 4 and 5 can be the lengths - in appropriate units - of the sides of a right-angled triangle. 3 5 4 The perimeter and area of this triangle are : Perimeter = 3 + 4 + 5 = 12 units Area = 1/2 ...

... 3, 4 and 5 can be the lengths - in appropriate units - of the sides of a right-angled triangle. 3 5 4 The perimeter and area of this triangle are : Perimeter = 3 + 4 + 5 = 12 units Area = 1/2 ...

... three philosophers who were to influence Pythagoras while he was a young man. One of the most important was Pherekydes who many describe as the teacher of Pythagoras. Another teacher of his was Thales who was said to have first ...

... number (n) Short side (a) Middle side (b) Long side (c) 1 3 4 5 2 5 12 13 3 7 24 25 4 9 40 41 5 11 60 61 Just by looking at the table, I can work out the formula for finding the short side of a Pythagorean Triple in terms of n. Just in case, I worked it out: 0 1 2 3 4 5 1 3 5 7 9 11 ...

... 52 = 5 x 5 = 25 122 = 12 x12 =144 132 = 13 x 13 =169 And so 52 + 42 = 25 + 144 =169 This is also true for the numbers 7, 24 and 25. 25 7 24 7 = 7 ...

... always even numbers. I can immediately see the formula to derive the shortest side length from the term number. The term multiplied by two add one equals the shortest side length. Let Shortest Side Length = SL Term = T Term Number = ...

... units ? The numbers 5,12,13 can also be the lengths - in appropriate units - of a right-angled triangle. Perimeter = 5+12+13=30 Area=?x5x12=30 This is also true for the numbers 7,24,25 Perimeter = 7+24+25=56 Area=?x7x24=84 I have put these results into a table to see if I ...

... probabilities for the questions we played the game to give us an idea of what th outcome should roughly be. Here are the results : ROLLABCROLLABC1WIN21WIN2WIN22WIN3WIN23WIN4WIN24WI N5WIN25WIN6WIN26WIN7WIN27WIN8WIN28WIN9WIN29WIN10WIN 30WIN11WIN31WIN12WIN32WIN13WIN33WIN14WIN34WIN15WIN35 WIN16WIN36WIN17WIN37WIN18WIN38WIN19WIN39WIN20WIN40WI N4115398 ABC72013 As you can see from this pie chart, in practice it suggests that B is ...

... 37 444 = 37 666 = 37 999 = 37 777 = 37 9 12 18 27 21 It seems that when all the 3 digits are the same number the answer to the problem is 37. Can I use Algebra to explain this? aaa=100a+10a+a =111a = ...

... 25 + 144 = 169 = 13² 7, 24, 25 7² + 24² = 25² 7² = 7 x 7 = 49 24² = 24 x 24 = 576 25² = 25 x 25 = 625 And so: 7² + 24² = 49 + 576 = 625 ...