Radians To Degrees

Opponents of pi mark special day

The mathematical constant pi is under threat from a group of detractors who will be marking "Tau Day" on Tuesday.

Tau Day revellers suggest a constant called tau should take its place: twice as large as pi, or about 6.28 - hence the 28 June celebration.

Tau proponents say that for many problems in maths, tau makes more sense and makes calculations easier.

Not all fans of maths agree, however, and pi's rich history means it will be a difficult number to unseat.

"I like to describe myself as the world's leading anti-pi propagandist," said Michael Hartl, an educator and former theoretical physicist.

"When I say pi is wrong, it doesn't have any flaws in its definition - it is what you think it is, a ratio of circumference to diameter. But circles are not about diameters, they're about radii; circles are the set of all the points a given distance - a radius - from the centre," Dr Hartl explained to BBC News.

By defining pi in terms of diameter, he said, "what you're really doing is defining it as the ratio of the circumference to twice the radius, and that factor of two haunts you throughout mathematics."

The discrepancy is most noticeable when circles are defined not as a number of degrees, but as what are known as radians - of which there are two times pi in a full circle. With tau, half a circle is one-half tau.

Dr Hartl reckons people still use degrees as a measure of angle because pi's involvement in radians makes them too unwieldy.

He credits Bob Palais of the University of Utah with first pointing out that "pi is wrong", in a 2001 article in the Mathematical Intelligencer .

But it is Dr Hartl who is responsible for the Tau Manifesto - calling tau the more convenient formulation and instituting Tau Day to celebrate it.

Kevin Houston, a mathematician from the University of Leeds, counts himself as a convert.

"It was one of the weirdest things I'd come across, but it makes sense," he told BBC News.

"It's surprising people haven't changed before. Almost anything you can do in maths with pi you can do with tau anyway, but when it comes to using pi versus tau, tau wins - it's much more natural."

Dr Hartl is passionate about the effort, but even he is surprised by the fervent nature of some tau adherents.

Converting between degrees and radians Silverlight Animations

Let's code up a couple of examples to take a look at a few of the concepts we've covered so far. We'll begin with a project that will start getting you used to the idea of converting between radians and degrees.

1. Open the DegreeRadianRotation project to code along. The project contains two circles, each with a radius of 100 pixels, as well as a couple of TextBlock labels so we can place some feedback on the screen.

2. Start in the MainPage.xaml.esfile by creating the DegreesToRadiansQ and RadiansToDegreesQ functions:

public partial class MainPage : UserControl {

public MainPage() {

InitializeComponent();

private double RadiansToDegrees(double Radians) {

double Degrees = Radians * 180 / Math.PI; return Degrees;

private double DegreesToRadians(double Degrees) {

double Radians = Degrees * Math.PI / 180; return Radians;

We're going to create two lines—one radius for each of the circles in the application. One will be rotated in degrees and the other in radians. The rotation of each circle's radius is based on the sine and cosine functions, which will be passed a changing angle.

3. We will need to track two angles and two rotation speeds—one expressed as degrees and the other as radians. To position the radius correctly, two Point variables are created to store the center of our circle elements. Add the following set of variables just before the MainPageQ constructor. Notice that the RadianSpeed variable, which will be used to calculate the radian-based rotation, is .01745. This is the equivalent of 1 degree.

public partial class MainPage : UserControl {

private double SinAngle = 0; private double SinAngle2 = 0; private double RotateSpeed = 1; private double RadianSpeed = .01745;

private Line SineRadius = new Line(); private Point CircleCenter = new Point(); private Line SineRadius2 = new Line(); private Point Circle2Center = new Point(); [...]

4. We need to do a bit of initial setup to get our radii to draw on the screen. Inside the MainPageQ constructor, just below the code that says InitializeComponent();, add the following code. These two blocks create the lines that are the radii for our circles. Both have a stroke that is 2 pixels wide. The first one has a blue color applied, and the second is colored red. Once the strokes have been defined, the lines are added to the canvas.

SineRadius.StrokeThickness = 2; SolidColorBrush SineStroke = new SolidColorBrush(); SineStroke.Color = Color.FromArgb(lOO, 59, 130, 255); SineRadius.Stroke = SineStroke; LayoutRoot.Children.

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