Plotting Pythagorean triples in a polar form

In summary, The conversation discusses different ways to plot the integer occurrences of a^2 + b^2 = c^2. The speaker suggests using polar coordinates and explains the process of finding the angle theta and radius c to plot in polar form. They mention difficulty with Mathematica and invite others to try. There is a further suggestion to plot in cartesian coordinates with x=c and y=angle, with a reminder to possibly scale up Y for better visualization.
  • #1
tdswenson
3
0
There are plenty of interesting plots that use various ways to plot the integer occurrences of a^2 + b^2 = c^2 such as making ordered pairs (a,b) and doing that for all such that a^2 + b^2 < [a really big number] and very interesting patterns are noted. My thought is plotting a polar analog. Consider the legs of a right triangle a and b, use tangent to find the angle theta that is opposite of b, then knowing the value for c (because it is a pythagorean triple) plot it in polar form (theta, radius) where theta is can be easily found and the radius is c.

I am new to mathematica, and am trying to get it to work with little success yet. I will continue to try. I am posting it if anyone else wants to take a crack at it. Sorry for any lack of clarity in my explanation above; I am in a hurry want to post this before I leave. Thoughts, advice, criticism, all are welcome!
 
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  • #2
Hi, tdswenson,
from your description it sounds like you'll get exactly the same graph as when plotting in cartesian coordinates with x=a and y=b.

Maybe your intention is to plot again in cartesian coordinates, but with x=c and y=angle. Note that you might need to scale up Y in order to see something, as your maximum c increases.
 

1. What is a Pythagorean triple?

A Pythagorean triple is a set of three positive integers (a, b, c) that satisfy the Pythagorean theorem, a^2 + b^2 = c^2. This means that the three numbers can form the sides of a right triangle.

2. What is a polar form?

Polar form is a way of representing complex numbers using a distance (r) from the origin and an angle (θ) in the complex plane. This is often expressed as z = r(cosθ + isinθ).

3. How do you plot Pythagorean triples in polar form?

To plot a Pythagorean triple in polar form, you can use the values of a and b to determine the distance (r) from the origin, and then use the Pythagorean theorem to find the angle (θ). You can then plot the point (r, θ) in the complex plane.

4. Can all Pythagorean triples be plotted in polar form?

Yes, all Pythagorean triples can be plotted in polar form. However, some may result in a complex number with an imaginary component, which means they cannot be represented on a traditional 2D graph.

5. What is the significance of plotting Pythagorean triples in polar form?

Plotting Pythagorean triples in polar form can help visualize the relationship between the sides of a right triangle and the complex numbers in the complex plane. It can also be useful in solving problems that involve finding the distance and angle of a complex number.

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