Maths Coursework on T-Shapes

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Maths Coursework on T-Shapes

        

        

In this maths coursework I will be investigating T-shapes, T-shapes exist in grids, like the 9x9 grid above. The blue highlighted shape is a the simplest T-shape in the grid. The number at the bottom of the T-shape is called the T-number; in this case the T-number is 20. The sum of all the numbers in a T-shape is called the T-number. This T-number is 37, 1+2+3+11+20=37. In the first part of the investigation into T-shapes I will try to find a formula that finds the T-total using only the T-number. Now lets recap on the basic facts about T-shapes.

  • The number at the bottom of the T-shape is called the T-number
  • The total all of the numbers in a t-shape is called the T-total.

        

In this investigation I will first find a formula to find the T-total using the T-number in a 9x9 grid, I will then use differing grid sizes to see what an affect this has on the formula. Then using this information I will find a formula, which will be true to all grid sizes. Then I will experiment with rotations and reflections on differing grid sizes to see what an affect it has on the formula. Then a Conclusion about T-shapes.

To find the formula, which will show the T-total with the T-number, I will first make a note of some of the T-totals in this grid.

  • 1+2+3+11+20=37
  • 2+3+4+12+21=42
  • 3+4+5+13+22=47
  • 4+5+6+14+23=52

The gap between each T-total on the grid is 5 so the formula might need to have a five in it somewhere to illustrate this. And the T-numbers go up by one each time. Because the gap between each T-total is five, I will attempt to find out the formula by multiplying the T-numbers by five and finding the difference between that and the T-total.

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  • 20x5=100
  • 21x5=105
  • 22x5=110
  • 23x5=115

The multiplied versions of the T-numbers go up by five each time as well as the T-totals, this seems to suggest that the formula will be derived from these two parts, because the difference between them on this grid will never be different. So if we subtract the T-totals from the multiplied T-numbers and then add the result to the formula, we should have the correct formula.

  • 100-37=63
  • 105-42=63
  • 110-47=63
  • 115-52=63.

The answers are all 63, another constant in the ...

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