An Investigation on T-Shapes

An Investigation on T-Shapes

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Category: Mathematics Essay
Subcategory: Geometry
Words: 456
Pages: 5
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Document details
Category: Mathematics Essay
Subcategory: Geometry
Words: 456
Pages: 5

T-shapes Investigation Looking at the 9-9 grid below and the T-shape drawn on it, The total number of the numbers on the inside of the T-shape is called the T-total 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990 The t-total for this T-shape is123112037So 37 T-total The number at the bottom is the T-number, So the T-number for this shape is 20 Tasks1) Investigate the relationship between the T-total and the T-number2) Use the grids of different sizes. Translate the T-shape to different positions. Investigate relationships between the T-total and the T- number and the grid size.3) Use grids of different sizes again, try other transformations and combinations of transformations. Investigate relationshipsbetween the T-total and the T-number and the grid size and the transformations. 1) Solution 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990 T69 5051526069282 T22345132247In the diagram below it shows the difference between the T-number and the other numbers. First is the T-shape in question 1231120 This is the T-shape and here is the Difference T-shape N-19N-18N-17N-9NThis shows the difference N T-numberIn the T on the previous page I have noticed that the first difference from N is 9 which is also the Width of the square.Ill put that idea into another T. Note W width number (9) N- (2W-1)N-2WN- (2W1)N-WN The formula for the Value of the T-total now is shown as5N-7WT-total 2) Different sizes and relationship I know this works for the grid 9 by 9 but Im not sure if itll work for any other grids because there is more intervals in between the first number of each line.Here is a test for a 10 by 10 grid 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100 T22123122240 I notice this is 3 more than 9 by 9 I predict this is from the each extra number in each row T694849505969275 I notice no similarities Method test 22x5110 - ...

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