Thursday, June 27, 2019
Pottery Meets Mathematics II
I found a bug in my MATLAB code for the pottery shapes in the last post, so those computational examples are not correct (but the math is). I actually found the mistake by building a five sided shape out of paper and seeing that it did not match the computational results. In my professional life, I would call this experimental model validation (or invalidation in this case). Code is fixed and now simulation matches reality.
Friday, June 21, 2019
Pottery meets Mathematics
Two of the things I really like in life come together. A type of construction I have used in the past is to make N symmetric, identical slab pieces (with N being 3 or 4 so far) and form them into a bowl. A recent example is show below (with N=4) and I think it turned out rather well.
What I thought would be fun is to figure out what the resulting form shape would be from a given piece shape and the "N". It was a fun bit of math shown below. There is another way you can derive it using rotations of curve tangents but this derivation is more my style.
What I thought would be fun is to figure out what the resulting form shape would be from a given piece shape and the "N". It was a fun bit of math shown below. There is another way you can derive it using rotations of curve tangents but this derivation is more my style.
I implemented a simple approximation in MATLAB and plotted out a few examples. The first is with N=4 and f(s) = sqrt(1+s) - 1 with s going from 1 to 4:
and the second with f(s) = sqrt(1+2*s) -1:
You can see that the second has a flatter bottom -- completely flat at the centre since the derivative of f at s=0 is 1 (matching the N=4 case of 45 degrees). Note that you don't need to start the piece at s=0. You can start with s>0 and add a flat bottom (or anything else you want to do there).
I think I need better visualization of the resulting surfaces to be able to use this as a tool to help pick aesthetically pleasing shapes. If I got really involved, I could generate the shapes for (small scale) 3D printing as a way to explore designs.
Tuesday, June 4, 2019
Clint's Game of Thrones
Warning: this post contains spoilers of the last season of the TV show, Game of Thrones.
Game of Thrones is an eight season fantasy-themed TV show based on the novels by George RR Martin. If you don't know that, I am not sure why you would know me or read my blog. The series of novels is unfinished, and unlikely to be finished before Martin's death. The novels are a bit variable in quality but overall very good. The TV series has also varied in quality, with a steady decline after the action passed what was in the written texts. The final season was abysmal. My two main criticisms: Daenerys (who I was hoping would claim the throne in the end) was steadily portrayed through the show as an empathetic ruler trying to do the right thing and then went psycho in the last two episodes; the Über boss (the Night King) was defeated like a chump in episode three of six, so the rest of the season was anticlimactic. The dialog in the end scenes of the last episode was amateurish (although the response to Sam's call for democracy was amusing).
Despite these criticisms I really enjoyed the last season because I was not watching Game of Thrones, I was watching Clint's Game of Thrones. My friend Clint has had me and another friend over to watch the last few seasons. We have had a delayed start to each season, timed to be able to watch two episodes a week. He has a projector, so we watch on a big screen. There is alcohol and he orders food for us. Appropriate mockery is encouraged, and it was almost constant this last season. We amused ourselves with our growing outrage at the course of the plot. Clint was almost weeping in frustration during the later episodes.
The right kind of bad show can be quite enjoyable when watched in a group. Two others I remember are Twin Peaks 90-91 that I watched with fellow graduate students in NYC, and V in the Summer of 1983 in a Carlton dorm where I was staying for a Summer job at the NRC lab in Ottawa.
Game of Thrones is an eight season fantasy-themed TV show based on the novels by George RR Martin. If you don't know that, I am not sure why you would know me or read my blog. The series of novels is unfinished, and unlikely to be finished before Martin's death. The novels are a bit variable in quality but overall very good. The TV series has also varied in quality, with a steady decline after the action passed what was in the written texts. The final season was abysmal. My two main criticisms: Daenerys (who I was hoping would claim the throne in the end) was steadily portrayed through the show as an empathetic ruler trying to do the right thing and then went psycho in the last two episodes; the Über boss (the Night King) was defeated like a chump in episode three of six, so the rest of the season was anticlimactic. The dialog in the end scenes of the last episode was amateurish (although the response to Sam's call for democracy was amusing).
Despite these criticisms I really enjoyed the last season because I was not watching Game of Thrones, I was watching Clint's Game of Thrones. My friend Clint has had me and another friend over to watch the last few seasons. We have had a delayed start to each season, timed to be able to watch two episodes a week. He has a projector, so we watch on a big screen. There is alcohol and he orders food for us. Appropriate mockery is encouraged, and it was almost constant this last season. We amused ourselves with our growing outrage at the course of the plot. Clint was almost weeping in frustration during the later episodes.
The right kind of bad show can be quite enjoyable when watched in a group. Two others I remember are Twin Peaks 90-91 that I watched with fellow graduate students in NYC, and V in the Summer of 1983 in a Carlton dorm where I was staying for a Summer job at the NRC lab in Ottawa.
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