# (How do I solve this formula?) Formula for Rounded Corners

I'm learning how to properly design app icons for iOS. A portion of this requires some knowledge in a formula that I've never seem before. Below is an image of the formula I'm trying to solve. For me, math is something I struggle with. How would I solve this? What are the lines around the $x$ and number? I believe the size (width $\times$ height) is what is input into the $x$. Is this something that I can solve using a calculator?

I've also seen the formula in this form $x^4+y^4=r^4$. Is this the same formula in the photo?

(Continued)

I tried the following $|\frac{120}{60}|^5+|\frac{120}{60}|^5$ and got $64$. Seems really high and actually isn't the radii I'm looking for. Any thoughts?

• those lines are absolute value bars (usually function $abs$ in programming). The formula in the image is different from $x^4+y^4=r^4$ – Vasya Dec 14 '17 at 4:21
• Thank Vasya for your reply. In the formula I used on paper |120/60|^5+|120/60|^5 is that the correct output or should I be getting a different number? – user513420 Dec 14 '17 at 4:30
• @miler: see my answer. But $x^4+y^4=r^4$ will also work, just corners will be more rounded. – Vasya Dec 14 '17 at 4:46
• @Vasya I'm still getting a very high number. Which tells me I'm doing looking at this wrong. So, if I do 120^4+120^4 I should get the radius? Is that the entire shape or for each corner? – user513420 Dec 14 '17 at 4:54
• In which sense do you want to "solve" this, and why? If you want to use it in an app, you'd be more interested in how to draw it programmatically. – Professor Vector Dec 14 '17 at 8:44

It looks like the formula to create the image on the paper is $|x^5|+|y^5|=1$ because when $y=0$, $x=1$. You need to express $y$ in terms of $x$:
for $0 \le x \le 1$ it will be $$y=\pm\sqrt[5]{1-x^5}$$ for $-1 \le x \le 0$ it will be $$y=\pm\sqrt[5]{1+x^5}$$
Varying $x$ from $-1$ to $1$ and calculating $y$ you'll get points for your drawing.