Graph Florets of a Flower Take a look at this chamomile flower:



Pretty, isn't it? Well, what if I told you that this wasn't actually one flower?

A lot of flowers (including sunflowers, chamomiles, daisies and others) actually consist of many very small flowers (the black dots on sunflowers) on a flower head. These miniature flowers are called florets, and they are arranged in a very special way.

Basically, the nth floret's position on a flower head is (in polar coordinates):





where c = 1 (Note that 137.508 degrees = golden angle. You don't have to use this exact precision.)

This causes the florets to be formed in a spiral called Fermat's Spiral. The positioning of the florets also is connected with Fibonnaci numbers, but that's a tale for another time.

So, here's the challenge. Given an integer n as input, calculate the positions of the first n florets and plot them. This is graphical-output, so I do actually want you to display the points in either a window of some sort or outputted as data in some common image format to STDOUT or a file. Other than that, this challenge should be fairly straightforward. It's code-golf, so shortest code wins. GLHF!

Here is a sample picture of what an output might look like:
TI-BASIC, 34 bytes
For the TI-83+/84+ series of calculators.
Input N
2πe^(-2sinh⁻¹(.5→θstep
AnsN→θmax
&quot;√(θ→r₁
Polar                      ;Displays polar mode graphs to graph screen
Dot                        ;Prevents lines from connecting points
DispGraph                  ;Displays graph screen

This considers the dot at the origin to be the 0th dot.
Thanks to the one-byte sinh⁻¹( token, 2πe^(-2sinh⁻¹(.5 is a short way of getting the golden angle in radians. This is derived from the fact that e^(sinh⁻¹(.5 is the golden ratio.
Here are screenshots for N=50.
(Yes, that's a 96x64 monochrome display on a TI-84+. The newer color calculators have a resolution upgrade, but still have only 3.7% the pixels of an iPhone.)

Press TRACE to step through each point.