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# Polygonal and square numbers

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Published on: Mar 4, 2016
Published in: Education
Source: www.slideshare.net

#### Transcripts - Polygonal and square numbers

• 1. Polygonal and square numbers Authors: Mihai Iulia Nicole, Stefan Alexandra Elena, Brumaru Alexia Maria, Joe Stefania Silvia
• 2. A polygonal number can be represented by points in a polygonal shape. The first number in the sequence is always 1, followed by the second number which is the highest point from the polygonal shape representation. The third number is obtained by extending the two sides from the previous number completing with another higher point (named vertex) if it is necessary.
• 3. The sum of vertexes from the resulted shape is the third polygonal number. These are a few examples of polygonal numbers’ categories: triangles, squares, pentagonal and hexagonal.
• 4.  Definition: A number is a perfect square number if it is equal with the square of a natural number.  FORMULA: k Є N n= k2 The square numbers exist also in the multiplication table: 4 is the square of 2, 64 is the square of 8. Basically the perfect square numbers are on the diagonal of the multiplication table. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 2 4 6 8 10 12 14 16 18 20 22 24 26 28 3 6 9 12 15 18 21 24 27 30 33 36 39 42 4 8 12 16 20 24 28 32 36 40 44 48 52 56 5 10 15 20 25 30 35 40 45 50 55 60 65 70 6 12 18 24 30 36 42 48 54 60 66 72 78 84 7 14 21 28 35 42 49 56 63 70 77 84 91 98 8 16 24 32 40 48 56 64 72 80 88 96 104 112 9 18 27 36 45 54 63 72 81 90 99 108 117 126 10 20 30 40 50 60 70 80 90 100 110 120 130 140 11 22 33 44 55 66 77 88 99 110 121 132 143 154 12 24 36 48 60 72 84 96 108 120 132 144 156 168 13 26 39 52 65 78 91 104 117 130 143 156 169 182 14 28 42 56 70 84 98 112 126 140 154 168 182 196
• 5. 18 is not a square number because there is no number multiplied by itself that results 18. 9 is a square number because number 3 multiplied by itself results 9. Observation: The last digit of a square number can be: 0,1,4,5,6 and 9 but not 2,3,7,8. The reverse is not true- a number having the last digit 0,1,4,5,6 or 9 is not always a perfect square number. 24, as an example, is not a square number even the last figure is 4.