# How to create a curved triangle of specific dimensions?

I'm trying to make a triangle where all the sides are curved outward, like a Reuleaux triangle, but the sides must be of a specific length. The length must be measured along the curve, not from end to end in a straight line, and the shape must be a specific vertical height. Is there a way to do this, including using any software or websites? I've included a picture to show what I'm trying to do. Thank you!

• there are lots of software that can do this it really comes down to budget and what you expect the user interface to be. Also depends on how much calculation you want to do... So without any limitting qualifications the list of apps that can do this is staggering, hell even notepad can do this. Just so we are clear the app that i would likely use for this costs 2000\$ a year Nov 1, 2022 at 5:18
• This seems more like a math problem. By the way, there are many solutions. Do you have other constraint? Nov 1, 2022 at 6:49
• @KrisVanBael there is an two categories of CAD applications that deal with solving constraints based drawings, and a few math applications for solving geometry problems. So no math needed really, but getting started might be too much work though as you still need to understand the gist of the math behind it. Also, im not in front of my computer but seems to me if the arcs are centrally symmetrical like the picture seems to be then it is fully constrained. But yeah still more than 30 apps that could fit the bill. Nov 1, 2022 at 7:02
• CAD software may be more suitable than graphic design software if you need accuracy. Vector software used for graphic design can't really do perfect circles or arcs, because they use Bézier curves to approximate them. However, this is actually a geometry question more than anything else. It may or may not be possible to have all those exact measurements form a triangle. I think Mathematics Stack Exchange would be more suitable for this. TBH. Nov 1, 2022 at 10:55
• I see this question gets a few downvotes. I think it lies just within the borders of graphic design. We should allow a few of these. Geometry is useful for graphic designers. Asking about how to find the center of a rectangle wouldn't be regarded as off topic, would it? Is this just too complex? Nov 1, 2022 at 19:53

There are lot of software that can do this. Mostly CAD software, but both geogebra and solvespace are free. On commercial space anything parametric that has a 2D solver does this for you AutoCAD, Catia, Creo, Fusion 360 Solidedge, Solidworks...

So example from Creo. A bit depending on the particulars of your constraints the system seems to have zero, one or two degrees of freedom. So if we assume that the arc is symmetrical across the middle of the line we get according to the CAD one degree of freedom. Ive chosen to lock the freedom on a dimension of the angle at the top at 130 degrees. Since that seems prudent for a cutting pattern which is expect this to be but YMMV on particulars. See picture below:

And here i asked it to do a give me from 100-160 angles in 10 degree increments a vector format (2 commands):

Now is Creo the app to choose? Perhaps not, its not a terribly good presentation drawing software so you would still need inkscape or illustrator as a pair for it. But I'm merely pointing out that this is relatively easy in CAD application horrible in nearly anything else. Mostly its out of the price range for most users out there. If you want one package that does both good free drawing and parametrics consider AutoCAD.

Anyway this is not graphic design anymore

• lol@ 'this is not graphic design anymore'. Then take it to Mathematics instead of answering it here :P Nov 2, 2022 at 10:00
• @Vincent its not mathematics either. Maybe engineering but i have a feeling they would just ignore it. Anyway softwarerecs.se would be the thing. But as long as we accept softwarerecs why would you have to be limitted to illustrator, inkscape, corel draw and affinity designer. But yes i debated wether to answer or not ;) Nov 2, 2022 at 15:41
• Hey, I am equally bad for giving it an upvote. Nov 2, 2022 at 16:14

The actual graphic design seems already been done - you have decided what shapes are needed. The question asks only some hints how to draw them.

You have already got something, but here's a little more. The case becomes possible to be worked with Excel worksheet if you have good high school level geometry, trigonometry and plane vector algebra knowledge and you accept 2 radically simplifying assumptions based on your drawing. The assumptions are:

• The shape is left-right symmetric, it's enough to solve one half of it
• the arcs meet perpendicularly in bottom corners

The latter assumption is so restricting that you need to solve only one vector equation which splits to 2 scalar equations to x and y components.

The result with your given side lengths is shown in the right half of the next image:

There's a rectangle and 2 circles drawn to its opposite corners. The green area is a half of your shape. The numbers are inches.

The only equation which needs to be solved presents the brown vector (see the left half of the drawing) in two ways: The brown vector is the dotted magenta line rotated counterclockwise along the known length arc. As well the arrow tip of the brown vector can be reached by falling downwards from the center of the red circle to the top of the 6,5 inch long line.

The key observations to see that one vector equation is enough is to see that

• the magenta lines make a rectangular triangle
• angle A is as big as angle B due the perpendicularity of the angle sides.

I am not going to tease people here with equations. If one could understand them he as well writes them in a minute based on the given text explanations. I put Excel solver to search the right radiuses to the circles.

• question asks for software recommendation for drawing, are you suggesting excel? Nov 3, 2022 at 4:54