# Reuleaux Triangle #1 (Basic)

## Creator

Jedidiah Butler (@MathButler)

## Difficulty

Basic

## On to the Challenge!

Can you create the following graph using desmos.com or some other graphing tool? If you’re victorious, leave us a note in the comments when you’re done.

This is an early step toward the advanced version that looks more rounded inside. Lists are used to plot multiple lines.

To define a list, try the following:

This will essentially give * a* 13 different values.

Can you find the list values for this 3 element list and recreate this graph?

I did not know how to graph a triangle so I kinda didn’t do that part right. Every thing else seems to be correct.

x=.6

x=1.35

y=-|1.5x-1.5|+1.5

y=-.6x+.8

y=.6x+.36

y=-.6x+1.55

y=.6x-.4

Great start!

Many of these lines uses square roots (equilateral triangle). Try to be as precise as possible.

To draw the triangle itself you can use curly braces for domain and/or range restrictions (http://youtu.be/EnxldgRyUJs) .

I got pretty close but there is a slight difference between the two graphs that I can’t seem to fix.

x=1.26

y=-I1.5x-1.5I+1.5

x=.74

y=-.6x=.8

y=.6x+.36

y=.6x-.4

y=-.6x+1.55

y=0

I tried my best doing this and tried to get precise measurements, but due to the image, I couldn’t. The answers I got were:

x=1.26

y=-I1.5x-1.5I+1.5{x>0}{y>0}

x=0.74

y=-0.6x+0.8

y=0.6x+0.36

y=-0.6x+1.55

y=0.6x-0.4

y=0{0<x<2}

This is the most precise reuleaux triangle I got. Also, for those who don't know, the braces that I have put behind two equations are restrictions, also know as Domain and Range.

I think it can be done this way:

https://www.desmos.com/calculator/oef1cy3abj

This is more in the spirit of trying to create the equilateral triangle. Good use of sqrt() for precision.

x=.68

x=1.32

y=1.72x {0, 1}

y=-1.72 (x-2) {1,2}

y= 0 {0,2}

y= .58x +.38

y= .58x – .38

y= -.58x + .78

y= -.58x + 1.53

x=.67

x=1.32

y=.59x+.36

y=.61x-0.4

y=-.57x+.78

y=-.55x+1.5

y=0 (0<x<2)

y= 7/4x (0<x<1)

y=-7/4x+3.5 (1<x<2)

The graph consists of nine lines (no list), but it’s an exact

https://www.desmos.com/calculator/hjiksxrtwa

I’m not sure how to add restrictions so I just worked around that. It took a few tries to make everything line up, but it turned out pretty good.

y=|1.5x-1.5|+1.5

y=0

y=.6x-.4

y=.6x+.36

y=.6x+.8

y=-.6x+1.55

x=1.35

x=.6

y=(x/1.7)+.4

y=0

y=(5/3)

y=-(5/3)x+(10/3)

y=-{x}/{1.7}+.84

y=-{x}/{1.7}+1.55

x=.68555

x=1.3

These are the answers i got. I wasn’t sure how to make the a=[-6] stuff, but i think i still got it right

https://www.desmos.com/calculator/stpxn47cwp