Count the Pegs
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My task was to find 3 equations, that would give me an answer, if I had certain information. The first was to find one that if you knew that there were four pegs on the boundary, and none on the interior, you could get the area. The second was if you knew that there were 4 pegs on the boundary, and you knew how many were on the interior, you could get the area. And last, if you had the number on the interior, and the number on the boundary, you could get the area.
Process
The first two equations, were a preparation for the final, building up towards the complete idea. This helped, because I could complete the first two pretty quickly.
For Freddie I drew a 3 column T-Table, with a drawing of the figure, the number of Pegs (in), and the Area (out). I looked for a pattern between the in and the out, and quickly found one that made sense, and I worked it into a formula. I got X/2-1=Y. Where X is IN (number of pegs) and Y is OUT (Area). This works in all shapes
My task was to find 3 equations, that would give me an answer, if I had certain information. The first was to find one that if you knew that there were four pegs on the boundary, and none on the interior, you could get the area. The second was if you knew that there were 4 pegs on the boundary, and you knew how many were on the interior, you could get the area. And last, if you had the number on the interior, and the number on the boundary, you could get the area.
Process
The first two equations, were a preparation for the final, building up towards the complete idea. This helped, because I could complete the first two pretty quickly.
For Freddie I drew a 3 column T-Table, with a drawing of the figure, the number of Pegs (in), and the Area (out). I looked for a pattern between the in and the out, and quickly found one that made sense, and I worked it into a formula. I got X/2-1=Y. Where X is IN (number of pegs) and Y is OUT (Area). This works in all shapes