Introduction: Make an 8 Inch Circle Using a 6 Inch Rectangle

Picture of Make an 8 Inch Circle Using a 6 Inch Rectangle

In this instructable I will show you how to make a circle using a rectangle and have the exact center of the circle.

I will take this moment to give you a little background on how I came upon this little trick.
Perhaps this is taught somewhere in some classroom in the world, I don't know. Here is what I do know.

I was in the middle of building a Scrap Wagon you might ask what is a Scrap Wagon? Well it is a wagon that is made 99% from scrap material. My kids were complaining about how heavy all of their baseball equipment is to carry to the park, and yes it is heavy. So I decided to look into buying a wagon for them. After seeing the prices for a wagon I decided that I did not want to spend $70. I am talking Costo or Walmart yard wagon. I could have bought a cheap wagon for $30 but it would just fall apart.. When I buy something I buy something that it is going to last. So, no I didn't buy one.

I came to a point where I needed wheels, while shopping around, even at Harbor Freight, I couldn't find any for what I wanted to pay.

Sticking to the Scrap theme I decided to make the wheels out of wood. Yes wooden wagon wheels, crazy idea huh? Someone was throwing out and old water bed frame. This was perfect for the wheel because they are a 2 inches thick by 9 inches wide by 6 ft. long.

So finally I have the materials for the wheels. I was wanting a perfect circle with an exact center in the pattern. So I ran upstairs and loaded AutoCad 2000 on my PC and find out my SN is expired or some crap. So I D/L a couple free CAD programs, yeah they are crappy and won't put a circle in the very center. Can you believe that? So now I am a little miffed and I have spent way to much time on a CAD circle.

So I stopped and said "How did the Romans and Greeks do it"? They didn't have a CAD program. After sitting and thinking for a while I had an epiphany, Duhh, its so simple.

So one day I am substituting for an Algebra class with some Freshman and Sophomores I challenged them with the same problem. None of them got it, but some came darn close. I gave lots of clues and enjoyed seeing the concentration on their faces. When I explained it to them they each had their own epiphany.

I even gave the problem to a high school calculas class, they showed me everything about an 8 inch circle except how to make it.

So here it is "How to make an 8 inch circle with a 6 inch rectangle."

There is a complete video on the last page.

Step 1: Materails and Tools

Picture of Materails and Tools

Here is what you will need

(1) Pencil or other writing instrument
(1) 6 inch x 2 inch rectangle piece of wood
(1) Screw
(1) 12 inch ruler or other measuring device
(1) 9 inch square or larger piece of wood (or other material you want to cut or experiment with) i used wood
(1) Drill with drill bit

Step 2: In the Begining

Picture of In the Begining

We begin by measuring the dimensions.

1. Using the example below lets draw dimensions on the 1.5 x 6 inch piece of wood.

1.1 Find the horizontal center length of the wood rectangle and draw a line down the center of the rectangle. Do the math (1.5 inch / 2 inch = .75 inch center)

1.2 Measure 1 inch in from each end of the wood rectangle and draw a horizontal line.

1.3 Now you should have a total of 3 lines:
1.3.1 a line down the horizontal center of the rectangle
1.3.2 a line 1 inch in from the left side
1.3.3 a line 1 inch in from the right side

2.using the example below lets draw dimensions on the large 9 inch x 6 foot piece of wood .

2.1 Next using your large 9 inch x 6 foot piece of wood create a 9 inch square. We already know it is 9 inches wide so measuring from one end of the wood, measure 9 inches in and draw a line.

2.2 Next we need to find the exact center of the 9 inch square.
2.2.1 Measure 4.5 inches down and 4.5 inches over to create (4) 4.5 inch squares
2.2.2 Now we have the exact center of the square (You could have drawn from corner to corner to also find the center, but then we would not have 4 little squares and I like squares).

3. Lets take this time to grab our drill and small drill bit and drill a pilot hole in each of the 3 line intersections.
3.1 Drill 2 holes in the 6 inch rectangle and one in the center of the 9 inch square.

Step 3: Placement of the New Tool.

Picture of Placement of the New Tool.

In the last step we measured and drill two holes in the rectangle. We are giving that a name now lets call it a "Jig" and lets place it on our 9 inch square.

1. Grab you screw and put it through on e of the holes in you jig

2. With the screw in the jig hole, place the screw point into the pilot hole in the 9 inch square.

3. Screw the screw into the wood. Don't tighten the screw down all the way, you don't want it tight, you want it to move easily.

4. Now you should have the jig screwed into the square. See the pic below.

Step 4: Lets Make the Circle

Picture of Lets Make the Circle

Now that you have the jig screwed into the center of the square, grab your pencil and place it in the other hole of the jig.

Make sure your the lead of the pencil reaches through to the square and then rotate the jig in a complete circle and you will have drawn and 8 inch circle with a 6 inch rectangle.

Step 5: Review Measurements

Picture of Review Measurements

Take a minute to review your measurements.

Step 6: The Video

Picture of The Video
This video is about 5 minutes long but entails each step of the process. You will see me make an actual circle with a rectangle.


broken board (author)2012-04-02

Nice idea
Could have used it yesterday.

But god dam I hope your woodworking skills are better than your videoing skills.
Giving me a dam head ache

mr.break_it (author)2009-10-03

if you need free software just use torrents like thepiratebay or mininova

sokamiwohali (author)mr.break_it2012-02-16

what was the point of this comment??

mr.break_it (author)sokamiwohali2012-02-17

I actually have no Idea. Sorry for my irrelevance.

sokamiwohali (author)mr.break_it2012-02-17

no prob...i was just wondering cause that seems like the most random thing on this ible. i would also not talk about the pirate bay or free torrents, it could get you in trouble in case a law official is trolling to look for things like that.

dadu2007 (author)2010-02-18

An easy way >

jack_savage (author)2007-09-26

no offense but im going to have to agree w/ kharmsengine you really havnt shown us anything new you say you are trying to educate high school students in the basics of geometry im just saying that i could have done this in 3rd grade or possibly below and why not just buy a compass, one would cost the amount of a couple screws or bolts also you dont need autoCAD to print off circles, heck i could do that in word

rocketman217 (author)jack_savage2009-10-03

he is just trying to show other ways on how to do it rather than buying a compass

not about being NEW, i could think of tons of ways to do it.....could i have made wooden wagon wheels, NO can i now....well i at least know how to now. would love to be able to do it. what is new anymore....i like the old fashioned the way it use to be kinna of stuff sometimes it takes someone really great to make us all remember the "duh" kinna things. like using the computer to do it and only u spent more time trying to get the computer to think like u, and u still couldnt get the computer to do it right ROTFLMAO i love it.

Mr. Rig It (author)jack_savage2007-09-26

You start with no offense but your sarcasm says otherwise. Well jack I have to disagree. The difference is that I have made mine from nothing, I made the tools to make the object that I needed that is what is new. Sure you could wire some LED's together in a flash light and call it an instructable hack but did you make the tools that enable you to make the flash light or the heat sinc used to solder the wires? I didnt have a compass and the objective is to use what you have on hand anyone can go an buy a compass thats easy, challenge yourself with this style sometime and you will have a better understanding. You might be able to print off a circle in MS word but you would not have the center of it, part of the objective was to have the exact center not just make a circle. So you think a 3rd grader or below can do it? Prove it, show me, go and find a 3rd grader and make a video and post it. I have 4 high schools that I work at and none of the students were able to do it c completely. But apparently you are gifted and special, or so you think. If it was easy then anybody could do it. Oh yeah I am offended. Hey heres a thought If you are going to post something negative why don't you provide balance and post something you felt you like about it.

iMac (author)2008-09-08

Because compasses do not work good?

Mr. Rig It (author)iMac2008-09-08

I didn't have a compass to work with and didn[t feel like spending money on one. So essentially I made my own.

theburn7 (author)2008-05-27

what is with all of the negitave comments? I thought this instructable was the "wittier" side of instructables

Mr. Rig It (author)theburn72008-05-27

Some people just don't appreciate my caveman genius :-) and Thank you for the compliment.

CapnTac (author)2008-04-16

That is really clever! Nice job!

Mr. Rig It (author)CapnTac2008-04-16

Thank you, I appreciate the positive comments.

unspecified (author)2008-03-31

Seems like you are reinventing the wheel here, as it were.

dontno (author)2008-01-29

Great instructionable. I use a 12 inch ruler, which I scribed a line down the center of, and when ever I need to draw a circle up to 24 inches I just drill a hole at the appropriate measurment for the radius of the circle, and begin drawing out the circle.

Mr. Rig It (author)dontno2008-01-29

Thank you, I ended up doing the same thing with a flat clear grid ruler that I bought. I have used it a few times now. It works very nicely. Thanks for the comments.

kikkoman7347 (author)2008-01-18 was a fine instructable. Others just aren't thinking through the original intent and situation, and more importantly your 'free will'. Living part of my life out in the back woods of third world countries, simple ideas are often the most ingenious. Good idea, good instructable.

Mr. Rig It (author)kikkoman73472008-01-18

Thank you, I am glad to see some people are starting to understand the idea of this instructable. Thanks again!

kharmsengine (author)2007-09-25

in other words...."how to make a compass from scrap wood" i do this on a regular basis in construction work....whats so special?

Mr. Rig It (author)kharmsengine2007-09-25

Making a compass from scrap wood, I did explain it like this at the end of the video. I like the other way I say it, I think it’s a better presentation. What is so special? Most people don't realize how to do it. I am sure that since you’re in construction work you use all kinds of math. I presented this problem to high school students in basic math to calculus and like I said some came close to getting it but none actually did. It’s a practical application of basic math and geometry. I guess my point is while some students can do math on paper others can't, some students excel with the actual hands on application (tactile learning). The special part is watching kids who hate math actually challenge themselves with a real world issue and enjoy it, especially the kids with ADD or ADHD and if I can get kids to get excited and challenge themselves to actually work on the problem, well.. That is what is so special, Also this is a simple trick that I haven’t seen taught anywhere but in construction. Hey why not post some of the stuff you have learned in construction, like the simple everyday stuff. I bet you have some cool tricks to teach.

kharmsengine (author)Mr. Rig It2007-09-25

thats a good point.....i guess it was just too obvious to far as posting contruction tricks...i dont all just seems too banal to post

berserk (author)kharmsengine2007-12-14

Hey, one guys junk is another guys treasure! What seems obvious to you may not to others. Once you know how, anyone can do it. Enough of the platitudes, if you can think of a construction trick that, when someone first showed it to you, made you slap your forehead for not thinking of it, chances are there are at least some folks on this site who would also like to hear about it.

Mr. Rig It (author)kharmsengine2007-09-25

Those are the things that the rest of us miss out on though. I have one that I am currently writing showing how I stuccoed my cinder block fence. I have another one that I am also working on where I tiled my floors. I was going to write one on how I laid a small pad of concrete, but I already have too many going on. I guess in short sometimes it is the little things, like the compass, that make the difference and it was fun to write. Anyway give it a shot, just start with a short one. Have a great day.

Sharad (author)2007-12-06

In my previous post I have mistaken to say circles of different diagonals. I am sorry it should be different diameters.

Sharad (author)2007-12-06

Your method of drawing a circle with a rectangle is fantastic. Although other methods are available you have shown it with whatever material was at hand. Also a rectangle being a rigid body a circle drawn with it will be more perfect than with a string where the pencil may wander a bit while drawing the circle. With the rectangle you can draw circles of different diagonals. Bring some more ideas like this Sharad

paulwal (author)2007-10-04

I think emellqui is right, the problem isn't stated very clearly. I would make a couple of suggestions to make the problem more relevant to a geometry class.

1. Instead of measuring 4.5 inches and drawing cross-hairs to find the center of the 9 inch board, simply draw the two diagonals and where they cross is the of squares.

2. Measure 4 inches from the center in any direction and make a mark.

2. Push a pin into the center, tie a loop in the end of a string, and place it over the pin. Place the point of the pencil on the 4 inch mark, wrap the string around the pencil near the point, and draw the circle. 4 inch radius = 8 inch of circles.

Mr. Rig It (author)paulwal2007-10-04

Paulwal, Thank you for the suggestions. After rereading my instructable and comments that you and others have made it is clear that the problem isn't stated clearly enough. I haven't given enough background on why I did it the way I did. I need to go back and rewrite it 1. Yes I could have made an X and found the center, I thought I had said that, maybe not though. However I would have still had to measure out a 9 inch square to do it. Perhaps I will give alternative ways in the rewrite. 2. Yes I could have used a string, however I didn't think of it at the time, plus I didn't have a string. I had to work with what I had which was a 6 inch piece of scrap wood. The wood provides more structure than the string and it is easily reusable and I can drill different lengths holes into it and use it over and over. When I say more structure I mean it is going to give me a smoother circle, my pencil lead is not going to deviate to a different angle or elongate my circle on accident because of the way I hold it. Honestly I haven't tried the string method so I don't know it the deviation would occur, but it is my theory that it would. I needed all 4 of my wheels to be smooth. Thanks for the input, it looks like a rewrite is needed. Have a good day.

emellqui (author)2007-09-25

Claiming to use a rectangle to produce a circle is probably what confused the students. Believe it or not, I was able to do this with a trapezoid, triangle, octagon, and a piece of string.

Mr. Rig It (author)emellqui2007-09-25

Exactly, I can use a circle and do it as well.I am glad that you used the other shapes and the string. It's not to confuse them its to help them think outside the box. I want them to see for themselves not everything is as it seems or its not as hard as it seems. It is also a exercise for them to follow instructions, since most people live in a paradigm it can be difficult for them to overcome.

About This Instructable




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