These conclude my theory that opposite rotations are opposite signs
After these readings, I worked out equations for the T at 90°and 270° and arrived at the equations:
90°: N=5N+7
270°: 5N-7
After these initial set of results I worked out that the opposite T’s were always positive and negative:
0°:Negative
180°: Positive
90°:Positive
270°:Negative
This find, now enabled me to get through work quicker, but to make sure my prediction was correct I checked it on other T’s and it worked!
After this work, I moved more on to question two. Firstly, I experimented with the grid size and found the following results:
After compiling this table I worked out a formula for any regulation sized T in any grid at 180° and 0° this was:
5N+OR-7G
The G in this equation stands for Grid type i.e. 9,10,or 11.
For the 90° and 270° the Equation is the same;
5N+OR-7
After another look at the equation, I worked out that the five was in relationship with the number of squares in the T so (letting x be the number or squares) the equation is
XN+or-7G
To test this theory, I tested it on a 6-squared T, thus changing the form of the T so that it looked like:
∴ 6*21-7*9 = 63
This, Unfortunately Didn’t work, however, I made a table using only this type of T, the results were:
I tried to work out a formula for this type of T shape on 0° and 180° and came up with:
6N+or-9G+2
This time, however, the 90° and 270° were not constant and so I tried to work out a formula however there were no set formulas.
Now I moved further on into the depths of question 3, I used proportional change to see if I could find any relationship between the similar shapes,
So I tried:
After taking a series of readings from this shape I put the results into tabular form:
Now I will make a bigger enlargement to 13 squares:
Now I will go onto 17 squares, the reason why I am taking a lot of readings for these is to make sure of a general formula, when and if I get one.
From these results, I will now try to work some formulas
From this I can positively say that the equation involves a relationship between N and the grid type (x). However I cannot find a relationship with the N numbers.
I am now moving on to the other ideas of spreading the lower middle strand of the T to try and find a formula.
63 108 162 225
45 54 63
9x 9x
So after this I can say that the answer works out as 4.5x
Conclusion
For me this has been an exiting investigation. However I think I have not worked out enough of the formulas or explored deep enough. I got on to investigating question 3 but I worked on it with basic T shapes and with not such sophisticated advanced methods. However I feel I could have tried to work a bit quicker and found more time. I worked on questions one and two with efficiency and I believe that my work was detailed and well structured however, I got mixed up and never really had any structure to my investigation. I worked out the fundamentals involved in question three well and found sufficient answers.
