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

Rotation Of "T"- Shapes Clockwise

Extracts from this document...

Introduction

Rotation Of “T”-Shapes Clockwise

I shaded “T”-shapes on all the girds from 5 by 5 to 10 by 10, so that I could make a sequence and then find the formulae for all the grids. I rotated the “T”-shapes 90° clockwise until I had made a full rotation, (refer to diagram 1A) but did not change the “T”-number as I rotated the “T”-shapes.

 I then drew tables to show the “T”-numbers and the “T”-totals for the grids.

 Once I had drawn the tables and calculated the “T”-totals for all the grids I realised that there is a difference of 7 between the differences of “T”-totals as the grid size increases by one. E.g. In the 5 by 5 grid there is a difference of 42 between the “T”-totals of the “T”-totals of the first rotation and in the 6 by 6 grid there is a difference of 49 between the “T”-totals of the first rotation. 49-42 = 7 (refer to diagram 1B.) After I had

...read more.

Middle

“T”-total = pt + ( 7g + 7 )

               = 33 + ( 42 + 7 )

               = 33 + 49

               = 82

“T”-total = pt + ( 7g + 7 )

               = 36 + ( 7g + 7 )

               = 36 + ( 49 + 7 )

               = 36 + 56

               =92.

 This formula worked for both grids so I concluded that this was the correct formula for the first rotation.

 Now I needed to find the formula for the second rotation. From the information I had from the tables I had drawn I realised that the difference between the “T”-totals of the second rotation was less than the difference between the “T”-totals of the first rotation. So I subtracted the difference between the “T”-totals of the second rotation in the 6 by 6 grid (35)from the difference between the “T”-totals of the first rotation of the 6 by 6 grid (49) (refer to diagram 1B). 49 – 35 = 14. After I found that there was a difference of 14 I knew that there was there was a difference of 7 between 7g which for the 7 by 7 grid is 49 and 35.This was because I had added 7 to 42 to find the formula for the first rotation. So if you imagine 35, 42 and 49 on a number line. Then there is a difference of 14 between 35 and 49 and 42 being the mid-point between the two numbers.

...read more.

Conclusion

               =134 – ( 49 + 7 )

               = 134 –56

               =78  this is correct so I tried to use the same formula on the 8 by 8.

“T”-total = pt – ( 7g + 7 )

               = 151 – ( 56 + 7 )

               = 151 – 63

               = 88  this was correct so I concluded that this was the correct formula for the third rotation.

 When I was looking for the formula for the fourth rotation I realised that just like the first and third rotation. The difference between the “T”-totals of the second and fourth rotations where the same except that instead  of adding 42 you subtract 42 in the 7 by 7 grid ( refer to diagram 3). So as I had done to find the formula for the third rotation I subtracted  ( 7g – 7) from the previous “T”-total  to get the next “T”-total in the sequence. So I tried the formula

“T”-total = pt - ( 7g – 7 )

               = 78 – ( 49 – 7 )

               = 78 – 42

               =36 this was correct so I tried this formula on the 8 by 8 grid.

“T”-total = pt – ( 7g – 7 )

               =88 – ( 56 – 7 )

               =88 - 49

               = 39

Now I have found the formulae for all the rotations where pt = previous “T”-total in the and g = grid size

“T”-total = pt + ( 7g + 7 ) for the first rotation.

“T”-total = pt + ( 7g – 7 ) for the second rotation.

“T”-total = pt – ( 7g + 7 ) for the third rotation rotation.

“T”- total = pt – ( 7g – 7 ) for the fourth rotation.

 ( refer to diagram 4 )    

...read more.

This student written piece of work is one of many that can be found in our GCSE T-Total section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE T-Total essays

  1. T-Total. I will take steps to find formulae for changing the position of the ...

    The second part to the formula is the formula for moving the T shape up. This formula is 5x - y - 5zb. This seems the same as the formula for the downward movement, but there is a minus instead of an addition sign.

  2. T totals. In this investigation I aim to find out relationships between grid sizes ...

    We now need to use the same method with different grid size to make a universal equation. I have chosen a grid width of 5 as that has a central number as does a grid width of 9, but make it vertically longer as to allow room to express vertical translations.

  1. T totals - translations and rotations

    24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

  2. I am going to investigate how changing the number of tiles at the centre ...

    Total Tiles I am also going to investigate whether I can find a formula which give the total amount of tiles in my pattern, T, provided I have the pattern number. Table 2 Pattern: N 1 2 3 4 5 Total Tiles: T 12 24 40 60 84 +12 +16

  1. T-Totals. I will take steps to find formulae for changing the position of ...

    To find the rest of the formula I went back to my original T shape in the top left-hand corner of the grid. I replaced the T with x, which meant that the rest of the numbers in the T had to be substituted with something else to relate it to x.

  2. 'T' Totals Investigation.

    42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 'T' ? (X) 'T' Total (T) 18 34 29 89 50 194 61 244 T = X+(X-8)+(X-15)+(X-16)+(X-17)

  1. T-Total.I aim to find out relationships between grid sizes and T shapes within the ...

    - 19 + 20 - 18 + 20 - 17 = 37 The numbers we take from 20 are found, as they are in relation to it on the grid, as the T-Shape spreads upwards all numbers must be less by a certain amount, these are found by the following

  2. T-Total Investigation

    the following method; As there are 5 numbers in the T-Shape we need 5 lots of 20, the number adjacent to 20 is 11 which is 9 less than 20, the other numbers in the T-Shape are 1,2 & 3 which are 19, 18 & 17 less than 20.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work