tag:blogger.com,1999:blog-2207789741693789296.post9125852211840861814..comments2024-03-28T09:23:46.097-04:00Comments on Cool Math Stuff: Pi vs Tau: Pi's RebuttalEthan Brownhttp://www.blogger.com/profile/09611695185154134251noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-2207789741693789296.post-61080075549842815532013-12-19T17:19:27.063-05:002013-12-19T17:19:27.063-05:00I completely agree with this. Mathematicians have ...I completely agree with this. Mathematicians have adapted to the number pi for centuries, and have clearly been able to advance as a result. Changing to tau would not ease things for them, but for the general public, and high school trigonometry students in particular. I very recently went through the unit in my precalculus class involving sine and cosine graphs, and I would convert every problem to tau just because I got confused every time I would do it with pi. I just presented a series of mental math workshops to fifth graders today, and I tested out a teaching bit that combined mental math with proofs and algebra. Hearing a fifth grader walk out saying "I'm really excited to learn algebra in high school" is about the best compliment I can get. By taking something that American society believes to be hard and boring like algebra and showing how beautiful it can be is a real inspiration to students. Tau is the gateway to do this with trigonometry and further mathematics, and that is certainly the biggest reason why this conversion needs to be made.<br /><br />I'm thrilled at the amount of commentary that this post has gotten. It's great to see that math is not strictly quantitative, but can have two (and even more) sides to each argument.Ethan Brownhttps://www.blogger.com/profile/09611695185154134251noreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-62357860843460685862013-12-19T17:03:22.585-05:002013-12-19T17:03:22.585-05:00Yes. A good point. I've mentioned this before ...Yes. A good point. I've mentioned this before to Pi supporters, but all they say is that all the HS people are stupid. There is no bad student, there is only a bad teacher (to certain limits. It isn' completely true, but it is true that a good teacher is more important than a good student).Anonymoushttps://www.blogger.com/profile/05096750855158217636noreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-44778915302079920882013-12-19T16:57:32.376-05:002013-12-19T16:57:32.376-05:00Huzzah! Why do we need infinite triangles when we ...Huzzah! Why do we need infinite triangles when we could have a properly defined circle?Anonymoushttps://www.blogger.com/profile/05096750855158217636noreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-59980279961787365672013-12-19T16:55:57.744-05:002013-12-19T16:55:57.744-05:00Yes, but who cares about area? Pists usually say t...Yes, but who cares about area? Pists usually say that it's unnatural to define a circle from using the center (because it's unmeasurable, which is clearly not the case for a bike wheel, for instance), but they then say they want to define a circle based on area? That is DEFIANTLY not better than the radius.<br /><br />It's kinda like barley corns. An inch is 3 barley corns (the long way). Who wants to define an important unit in barley corns? You may say that it's fundamental, since it relates to a simple physical object, but I object. Why not use something less arbitrary? Make it actually definable? How about some large power of 12 times the planck length? Why 12? Because we should use base 12. Throw out the old, bring in the new (I think the bosses will agree).<br /><br />We use a lot of deprecated numbers based on ancient physical objects and their traditions. We need to throw those out now that we know better.Anonymoushttps://www.blogger.com/profile/05096750855158217636noreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-3598725627213940632013-12-18T14:43:05.387-05:002013-12-18T14:43:05.387-05:00The biggest reason in support of Tau lies in secon...The biggest reason in support of Tau lies in secondary education. Every time I work with HS students learning trigonometric functions, the biggest obstacle is the period of 2pi. Getting them to truly understand that 3/4 of the way through a period is 3pi/2 (Wow, I still have to stop and think about that each time.) adds so much confusion. These non-mathematicians could envision 3/4* tau so much more readily. The Tau manifesto is not so much for the mathematicians but for the 16 year olds and we who teach them.<br /><br />I once showed Vi Hart's video to a pre-calculus student. Her only response was, "I'm pissed."Jeff Nagelhttps://www.blogger.com/profile/03695000011551761324noreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-51153072445509200182013-11-18T03:38:53.961-05:002013-11-18T03:38:53.961-05:00Tau isn't necessarily more natural; if you do ...Tau isn't necessarily more natural; if you do a little research, you'll find that pi was originally defined as the ratio between the area of a circle and the square of its radius.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-30057407313126353692013-08-17T15:18:29.394-04:002013-08-17T15:18:29.394-04:00Why not advance to the new "out of the box&qu...Why not advance to the new "out of the box" concept of rPi? It promotes a trigonometric understanding of the Pi ratio: http://www.aitnaru.org/images/Pi_Corral.pdf<br /><br />The 62.402887364309.. degree radius is consistent in all of the designs: any circle can be squared once this angle is known (the trigonometry proves this).<br /><br />What is rPi? The geometric complement to Pi (all of the known digits of Pi can be substituted into the formula).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-9920061357935900772013-02-14T00:48:41.220-05:002013-02-14T00:48:41.220-05:00The very definition of a circle is all points on a...The very definition of a circle is all points on a plane equidistant from an origin. π is wrong. τ makes more since. The greatest victory of π is a terrible failure:<br /><br />a = πr^2<br /><br />We derive this as the limit of of stuffing an infinite number of isosceles triangles whose base is on the circle and whose acute ange is at the center. The formula for the area of a triangle is base times height divided by 2 (bh/2). Logically, the formula for the area of a circle after integrating those infinite triangles should be the radius squared times the circle constant divided by 2 ( a = (τr^2)/2 ).<br /><br />The point is that τ is the natural circle-constant. We should abandon π.<br /><br />I am a Tauist.Unknownhttps://www.blogger.com/profile/02725385230463619574noreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-10611947583523801532013-02-09T20:34:06.658-05:002013-02-09T20:34:06.658-05:00If "simplify" means get rid of any numbe...If "simplify" means get rid of any numbers out front, then <b><i>no constant can simultaneously simplify all formulas</i></b>. It's impossible. Even with just the two formulas for circumference and area of a circle, tau simplifies the circumference formula (τr), while pi simplifies the area formula (πr^2). And there are lots more formulas out there. The sphere volume formula is only simplified if we create a new constant β = 4π/3. Then we can just write volume = βr^3. The sphere surface area formula is only simplified if we create a new constant γ = 4π. Then we can just write surface area = γr^2.<br /><br />There is no universally "efficient" number. That's why it makes sense to use the universally "natural" number, which is tau.<br /><br /><br />Joseph Lindenberg<br /><a href="http://sites.google.com/site/taubeforeitwascool" rel="nofollow">sites.google.com/site/taubeforeitwascool</a><br />Joseph Lindenberghttps://www.blogger.com/profile/17937849128943764513noreply@blogger.comtag:blogger.com,1999:blog-2207789741693789296.post-86485265865784454222013-02-09T17:48:49.548-05:002013-02-09T17:48:49.548-05:00I was just directed to a part of the Tau Manifesto...I was just directed to a part of the Tau Manifesto where some Pi Manifesto points were addressed.<br />http://tauday.com/tau-manifesto#sec:getting_to_the_bottom_of_pi<br /><br />Let's see how pi supporters respond...Ethan Brownhttps://www.blogger.com/profile/09611695185154134251noreply@blogger.com