
Post by GeneticBlend on Dec 27, 2018 18:36:22 GMT 5
I've been working on the triangle puzzle on page 73. I think we are to come up with numbers for the shaded, smaller triangles within the larger triangles. I can determine numbers for the two tiny shaded triangles, but not for the other four shaded triangles. Does anyone think they have the same idea that I do?



Post by TxTH on Jan 11, 2019 16:04:41 GMT 5
Hey GB. Yes, I tried the number system too. These triangles (Sierpinski's gasket as we called it) are interesting. I taught my students how to create these triangles as a lab exercise in computer programming. It's cool watching the program build the multiple levels. Like you, I never could get the numbers to make any sense. Another technique i tried was to look at the position of the colored triangles. There are only two size triangles we need to be aware of and for simplicity I called them small and large. The small triangles we use with the small colored triangles and the large with the large colored triangles. So in my picture linked below I have circled a small triangle on the left that has a small triangle colored in it. If we label the three corners top, left and right, then the small triangle is on the left. The large circle example is also a left. www.dropbox.com/s/bq5uio98f6dakym/Triangle%20sizes.jpg?dl=0So looking at all of the coloredin triangles, from the top to the bottom you get: (SL = small left, SR = small right, T = top, LL = large left) SL, LL, ST, LL, ST or SLLLLL and STST. I just grouped them by their location. OK, now we have two sets. Think Morse code... small = dot . and large = dash  Again, we get two groups: if small is dot we get . .. = W I If large is dot we get ..  = D M Now, the lower triangle. You can invert it so it looks like the other triangle if you wish but it works either way. The groups we get if we invert it and go top to bottom are: SL, LR, SR, LL grouped: SLLL and LRSR = . . or . . = A N or N A Our possible combinations of the four letters are WI AN or DM AN Place them in any order you wish. There are 4 possible combinations of two letter groups that take them in order: WIAN, WINA, DMAN, and DMNA. That's as far as I got. Now what do you do with it? Did I lose anyone? lol

