Patrick Horgan It probably won't because inertia. But tau is obviously more sane in the most important cases -- i.e., the ones that people get hung up on when learning trigonometry.
The "π manifesto" reads very oddly to me. It accuses Hartl of cherry-picking examples to support his case, but then goes on to pick very obscure examples to support its own (Hartl has a rebuttal to parts of it in his updated manifesto -- http://tauday.com/tau-manifesto).
Mostly I see this as a bit of a lark -- it probably doesn't matter all that much in the scheme of things. But I do believe that proponents of the status quo fail to comprehend just how confusing that extra factor of 2 is to students early on. I think we could do a lot of good by changing early trig and analysis textbooks to use τ, explaining a bit later that π=1/2τ is still used in much of mathematics.
I am going to disagree with you a bit. Students will not struggle any more with one or the other. We are constantly given arbitrary things to learn and memorize. I can't see any difference. It seems an arbitrary thing.
Perhaps, but that wasn't my experience. I won't say it was a huge impediment, but it's more like the death of a thousand cuts. It's not just that 2π is just another symbol for τ. Rather, because we like to reduce expressions, the 2 smears out into everything around it. So one quarter-turn in radians becomes 1/2π. In other places, things that should be factors of 2 end up being factors of 4, obscuring the underlying truth and making it just a touch trickier to see.
The real clinchers for me were:
- The explanation of why A=1/2τr^2 makes sense (once you see it as integration, the truth of it just jumps out at you).
- Euler's identity. e^(iτ)=1 makes it so clear that "a rotation by one full turn equals 1". While e^(iπ)+1=0 is just confusing, because π only takes you halfway around the circle to -1.
Again, I realize it's quixotic, but I do believe the implications are slightly more significant than it might appear at first.
Henrik Ohlin I like C4D, it's pretty addictive...however I do have a bit of a problem with the chunky 3D forms. But is better than writing all the functions in different math dialects. I am familiar with python and ruby. Processing is a bit different.
Corina Marinescu So it's a python based project I'm guessing? That's cool. Not sure what the chunky 3D means though as I've never used c4d myself (kinda why I'm curious in the first place). As Patrick Horgan stated I'm completely Blender-based. But yeah, 3D in general is quite addictive.
I hear ya. Stick with what you got and know. Especially if you have all the bells and whistles I'm sure it will serve you well beyond what you intend to use it for (for now at least).. Although as wave to Patrick and him being a fellow blenderhead (it seems), I'd like to share this article with you which hints to what blender is being used for..
I love the part where the radian length wraps around the circle.
ReplyDeleteSomething you will be sharing?
ReplyDeleteThat should read "τ rad" at the end there :)
ReplyDeleteHas τ rad caught on yet? I've been seeing it for years. Are text books using it?
ReplyDeleteOh, and http://www.thepimanifesto.com/
ReplyDeleteAbsolutely love these types of posts! Thank you for sharing Corina!
ReplyDeleteNice reusing wikipedia graphics.
ReplyDeletePatrick Horgan It probably won't because inertia. But tau is obviously more sane in the most important cases -- i.e., the ones that people get hung up on when learning trigonometry.
ReplyDeleteThe "π manifesto" reads very oddly to me. It accuses Hartl of cherry-picking examples to support his case, but then goes on to pick very obscure examples to support its own (Hartl has a rebuttal to parts of it in his updated manifesto -- http://tauday.com/tau-manifesto).
Mostly I see this as a bit of a lark -- it probably doesn't matter all that much in the scheme of things. But I do believe that proponents of the status quo fail to comprehend just how confusing that extra factor of 2 is to students early on. I think we could do a lot of good by changing early trig and analysis textbooks to use τ, explaining a bit later that π=1/2τ is still used in much of mathematics.
I am going to disagree with you a bit. Students will not struggle any more with one or the other. We are constantly given arbitrary things to learn and memorize. I can't see any difference. It seems an arbitrary thing.
ReplyDeletePerhaps, but that wasn't my experience. I won't say it was a huge impediment, but it's more like the death of a thousand cuts. It's not just that 2π is just another symbol for τ. Rather, because we like to reduce expressions, the 2 smears out into everything around it. So one quarter-turn in radians becomes 1/2π. In other places, things that should be factors of 2 end up being factors of 4, obscuring the underlying truth and making it just a touch trickier to see.
ReplyDeleteThe real clinchers for me were:
- The explanation of why A=1/2τr^2 makes sense (once you see it as integration, the truth of it just jumps out at you).
- Euler's identity. e^(iτ)=1 makes it so clear that "a rotation by one full turn equals 1". While e^(iπ)+1=0 is just confusing, because π only takes you halfway around the circle to -1.
Again, I realize it's quixotic, but I do believe the implications are slightly more significant than it might appear at first.
I'm curious to know why you chose C4D for your project.
ReplyDeleteSure, why not blender? ;)
ReplyDeleteHenrik Ohlin
ReplyDeleteI like C4D, it's pretty addictive...however I do have a bit of a problem with the chunky 3D forms. But is better than writing all the functions in different math dialects.
I am familiar with python and ruby.
Processing is a bit different.
Corina Marinescu So it's a python based project I'm guessing? That's cool. Not sure what the chunky 3D means though as I've never used c4d myself (kinda why I'm curious in the first place).
ReplyDeleteAs Patrick Horgan stated I'm completely Blender-based. But yeah, 3D in general is quite addictive.
Blender also does great video editing.
ReplyDeleteNot familiar with Blender, I have all C4D modules and for now I'm gonna stick to this.
ReplyDeleteBlender is an open source solution.
ReplyDeleteI hear ya. Stick with what you got and know. Especially if you have all the bells and whistles I'm sure it will serve you well beyond what you intend to use it for (for now at least)..
ReplyDeleteAlthough as wave to Patrick and him being a fellow blenderhead (it seems), I'd like to share this article with you which hints to what blender is being used for..
http://3dprint.com/72094/3d-medical-model-save-spleen/