Geometry question

**Ray1936** · October-17-10, 09:20 PM

Well, it's been well over 50 years since my high school geometry classes, so maybe some of you whizzes can solve a minor problem for me.

I'm trying to make a game board that requires it to be an equilateral octagon. I'm starting with a 2' x 2' hunk of plywood. My first instinct was to mark down each side eight inches and the 16 inches, then connect the corner marks. Well, that doesn't work out. The cut side becomes much longer than the eight inches of the uncut side, and symmetry is lost.

So how do I measure that board to turn it in to an octagon equal on all sides?

**ndavies** · October-17-10, 09:34 PM

It works out the octagon sides need to be about 10 inches. The cut needs to be 7 inches from the corners.

http://buster2058.netfirms.com/octag...ayout_calc.htm

**MikeM** · October-18-10, 08:51 AM

Take a pencil and draw two lines connecting opposite corners - they will form an "X" intersecting in the middle. Use a compass or a nail and string to draw a circle, centered on the X, whose circumference is equal to the edge of the board - the arc of the circle should touch all four sides. Using a triangle or something similar, draw lines perpindicular to the "X" lines tangent to the circle - they will form the four "corners" of the octagon. Slice off those corners and you should have an equilateral octagon.

**Ray1936** · October-18-10, 10:53 AM

I'm gonna try that way later today, MikeM. Whaddahell, I'll take some photos and post, if not today, tomorrow. Interesting. Here's the board I'm trying to make.

**agirlintheD** · October-18-10, 11:06 AM

Originally Posted by MikeM

Take a pencil and draw two lines connecting opposite corners - they will form an "X" intersecting in the middle. Use a compass or a nail and string to draw a circle, centered on the X, whose circumference is equal to the edge of the board - the arc of the circle should touch all four sides. Using a triangle or something similar, draw lines perpindicular to the "X" lines tangent to the circle - they will form the four "corners" of the octagon. Slice off those corners and you should have an equilateral octagon.

Yep, all these years after high school and this still makes NO sense...lol!!!

**Det_ard** · October-18-10, 04:58 PM

1. Start with a square.

2. Draw the X from corner to corner

3. Put your compass point at any corner, and the compass pencil at the center of the X

4. Now rotate the compass left and right to make marks at the edges of the square

5. Repeat steps 3-4 for each of the other three corners.

The 8 edge marks are the corners of your octagon. Draw lines and cut.

**Det_ard** · October-18-10, 04:59 PM

This may help you visualize what I described.

http://jwilson.coe.uga.edu/EMAT6680/.../octconst.html

**MikeM** · October-18-10, 07:11 PM

Det_ard's method looks pretty good. I just pulled mine out of my behind - not sure if it would work.

**MikeM** · October-18-10, 07:14 PM

Attachment 7603

Sloppy photo editing, but...

Draw the green diagonals first,

then draw the red circle with its center at the center of the "X",

then draw the blue lines, perpindicular to the green lines, and tangent/touching the circle.

**Ray1936** · October-22-10, 03:06 PM

Thanks all....project complete thanks to your tips. Only I used a square with a 45 degree angle to mark the corners rather than drawing parallel to the X lines....was faster.

**Gistok** · October-22-10, 03:23 PM

As Det_ard showed... a compass is a very handy tool.

When I was in High School Geometry class many years ago, I used to hate the class. But then one day [[at home) I had a big stack of what were going to be thrown away index cards... and I thought gee what could I construct with them.

I ended up using a compass, and some scissors, and made a geodesic sphere from the individually round cut circles with the bisecting compass lines being the points where to start folding the paper edges... to make triangles and glue the overlapping edges together.... and did all it without using any written formulas!

Sadly my genius for making architectural forms ended there at age 15....

**MikeM** · October-22-10, 03:27 PM

Originally Posted by Ray1936

Thanks all....project complete thanks to your tips. Only I used a square with a 45 degree angle to mark the corners rather than drawing parallel to the X lines....was faster.

Oh good! I'm glad my method worked. I was wondering if you had a compass large enough to draw the circle. I have a beam compass for big jobs, otherwise it's a nail and string.

**Ray1936** · October-22-10, 04:16 PM

Nail and string worked just fine. I could have made a firm compass had I the ambition, but the shortcut was just fine for this old fart.

**gazhekwe** · October-22-10, 04:59 PM

That looks great! I am glad MikeM posted the how-to picture, I was having a time visualizing the steps.

**Ray1936** · October-22-10, 06:21 PM

The whole thing was an interesting mental exercise, to say the least! Now to sand the corners and drill a whole lot of holes.

**old guy** · October-26-10, 03:45 PM

Just out of curiosity Ray, what's the name of the game?

**Ray1936** · October-26-10, 04:04 PM

I know it as "marbles". Four marbles to a player, and use two decks of cards. You need an Ace or King to "get out of the start row" and begin travelling around the board. Cards count their pip value for moves, with Ace as one, Jack as 11, Q as 12, and K as 13 if not used as an out card. Fours can only move BACK four spaces. A Jack can have you 'switch marbles' on an opposing player. A seven can be split between multiple marbles. Got to have the exact number to get up the home row.

Cards are dealt five on the first deal; four on each subsequent deal,until the last deal, five again. Fun game for couples.

**jcole** · October-26-10, 04:42 PM

Originally Posted by Ray1936

Thanks all....project complete thanks to your tips. Only I used a square with a 45 degree angle to mark the corners rather than drawing parallel to the X lines....was faster.

Hey, you reinvented the STOP sign!!

**Ray1936** · October-26-10, 08:06 PM

Yes, and now I have four left-over 'yield' signs........

**old guy** · December-21-10, 07:33 PM

Ray, did you ever finish the marbles game?

**punky1** · December-21-10, 08:40 PM

Your posts about this game sent me on a hunt. Found a slightly different board configuration for you to try out next with interlocking pieces. Here is the site: http://cardsandmarbles.com/boardpieces.html

**Ray1936** · December-21-10, 09:51 PM

Originally Posted by old guy

Ray, did you ever finish the marbles game?

Yup, came out beautiful. It's buried in a closet right now behind a whole bunch of christmas presents, but I'll take a photo after that stuff gets cleared out.

**old guy** · March-17-11, 04:19 PM

Originally Posted by Ray1936

Yup, came out beautiful. It's buried in a closet right now behind a whole bunch of christmas presents, but I'll take a photo after that stuff gets cleared out.

uh.... ahem...uh..huh..