Started by SBR*, November 10, 2012, 07:05:05 am
Quote from: winkioI do not speak to bricks, either as individuals or in wall form.
Quote from: Barney StinsonWhen I get sad, I stop being sad and be awesome instead. True story.
Quote from: winkio on November 10, 2012, 11:27:52 amtau is a laughably naive idea
Quote from: Blizzard on November 10, 2012, 07:51:48 amSpoiler: ShowHideI wasn't convinced until I saw eiT = 1. Yup, 2 PI should be replaced with T, but only for understanding and teaching children about trigonometry, circles and waves. If you read up on Wiki about PI, you will notice how many representative formulas and attempts for calculation are important that PI stays PI. What the people don't understand is that math is messy. It's not always elegant and there aren't always elegant solutions or substitutes.I think it's really funny how the videos are biased as well. The area of a circle is r2 x PI. This means that using T would cause it to become either r2 x T / 2. And that's not confusing? There are many more formulas that use PI and not 2 PI. You're trading one demon for another, really.The only thing that may make sense is to use both. But that makes things more complicated again so nobody's really gaining anything.
Quote from: winkio on November 10, 2012, 11:27:52 amSpoiler: ShowHideAs a mechanical engineer who has setup and solved many rotational systems, tau is a laughably naive idea and is utterly and completely wrong.The discussion here is on choosing between pi, which is a radius-defined value, and tau, which is a diameter-defined value. Let's examine some definitions:RadiansThe word radian is used to describe an angle as a ratio of the length of the circular arc to its radius. One radian is when the circular length is equal to the radiusWith tau, we would have to call them diametans, and would now be the ratio of the length of the circular arc to its diameter. Now you might be saying that we could just draw the diameter in the picture above, because it is already a circle, but what about this next picture:There is no circle. The radius lies along the arms, with endpoints at the vertex and the intersection of the arms with the arc. The diameter is completely irrelevant, and should not be considered.Angular Velocity (rad/s)If something is spinning, it has a nonzero angular velocity. First, let's examine a case where both pi and tau will work: a wheel rolling on the ground without slipping. If I want to know how fast the wheel is rotating, I simply multiply the angular velocity by the radius of the wheel. For a wheel of radius 0.1 meters rotating at 20 rad/s, I can find that it travels at 2 m/s. In this situation, because the wheel is radially symmetric, I can do the same thing with tau diametrans. For a wheel of diameter 0.2 meters rotating at 10 diam/s, I can find that it travels at 2 m/s.What happens when the object does not have a radius? Let's say the rotating object is the arm of a baseball pitcher as the throws the baseball, and we want to find out how fast he throws it. If we measure the length from his shoulder to the palm of his hand, then we know the radius of rotation. Let's imagine we did this measurement and got 0.65 m, thus when we see that he rotates a quarter of a circle in 0.1 seconds, that is 5pi rad/s, so we know that he can throw the ball at 5pi * 0.65 = 10.21 m/s.Since a diameter is not always defined in the system, it would be incorrect to define the angle based on the diameter.Torque (Nm)Torque is the equivalent of force for rotational systems. The first thing to note right away is that equations already use the tau symbol to represent torque, so tau should fuck off and find a different name. Torque is defined as a force acting at a radius from a center of mass, orthogonal (perpendicular) to that radius. Yes, torque is defined based on radius, and can't be defined based on diameter. There is no such thing as a diameter to a center of mass, it literally doesn't exist. In fact, as you go further along in your math career, you will find that diameters are only a part of science and engineering equations, and are dropped entirely from the mathematics curriculum, because they are not an independent value, but are a function of the radius, and can be undefined in many cases.tl;dr: tau is a terrible idea, pi makes sense, radians are a ratio, not an arbitrary number that you can fuck around with.
Quote from: SBR* on November 10, 2012, 02:19:12 pm1/2Tr^2 shows a lot of resemblence to other formulas like K = 1/2mv^2 and U = 1/2kx^2.
Quote from: SBR* on November 10, 2012, 02:19:12 pmAlso, on T day, you can eat twice as much pie.
Quote from: SBR* on November 11, 2012, 07:48:16 amIn general, isn't 3/4pi a different angle than -1/4pi?
Quote from: winkio on November 10, 2012, 08:13:32 pm-pi/4 is a lot more intuitive than going the long way around for 7pi/4.
Quote from: Blizzard on November 11, 2012, 08:38:29 amQuote from: SBR* on November 11, 2012, 07:48:16 amIn general, isn't 3/4pi a different angle than -1/4pi?Yeah, that's what winkio said.Quote from: winkio on November 10, 2012, 08:13:32 pm-pi/4 is a lot more intuitive than going the long way around for 7pi/4.Wasn't the whole point of Tau being a more practical constant than Pi? As far as I can see, the only place where Tau really makes sense is a circle. A Sine wave can also be looked at 0, Pi, 2 Pi, etc. being the zero-points of the function. Sure, Tau may be a whole period, but that's it. It's called a period and that renders Tau obsolete in Sines.
Quote from: SBR* on November 11, 2012, 09:26:48 amIt's about tau being a more fundamental and therefore a more beautiful constant than pi, as c/r is more fundamental than c/D=c/(2r).
Quote from: winkio on November 10, 2012, 11:27:52 amRadiansThe word radian is used to describe an angle as a ratio of the length of the circular arc to its radius. One radian is when the circular length is equal to the radiusSpoiler: ShowHide
Quote from: Blizzard on November 11, 2012, 04:09:59 pmQuote from: winkio on November 10, 2012, 11:27:52 amRadiansThe word radian is used to describe an angle as a ratio of the length of the circular arc to its radius. One radian is when the circular length is equal to the radiusSpoiler: ShowHideAnd yes, it's 2 Pi radians. When angles are measure in degrees, it's 360 degrees. When they are measured in radians, it's 2 Pi radians. Saying that an angle is 2 Pi is the same as saying that a car has a velocity of 50. 50 what? Potatoes?@Ryex: What I was trying to say is that a full circle is 2 Pi radians which means there is a connection. It's not that they depend on each other, but there are things that depend on both of them.
QuoteCircumference is the linear distance around the outside of a closed curve or circular object. The circumference of a circle is of special importance to geometric and trigonometric concepts. However circumference may also describe the outside of elliptical closed curves. Circumference is a special example of perimeter.
Quote from: Ryex on November 11, 2012, 06:21:14 pmI think you completely missing the point the guy is making about tau.A Circle is defined as the set of all points a distance of r (radius) from a central point.Pi is the ratio of a circle's circumference to it's diameter (C / D)Tau is the ratio of a circle's circumference to it's radius (C / r)When you work with a circle you work with it's radius and in all but the rarest cases you don't care about the diameter. so why is the fundamental circle constant described in terms of the diameter and not the radius? This is the point of using TauThe second link is a hour long talk the man gives on the subject and it becomes quite clear (to me at least) that the links between aspects of geometry, trig, and calculus be come a lot clearer when you knowledge that Pi introduces a factor of 2 to the task of working with a circles, and that factor of 2 often masks important concepts in simplified functions.