For the last couple of days, I have been playing around with this geometry puzzle. If you have a student in geometry or higher math, I recommend you print out the original post (but not the comments — it’s no fun when someone gives you the answer!) and see what he or she can do with it.

[MathNotations offers many other puzzles for 7-12th grade math students. While you are at his blog, take some time to browse past articles.]

Thanks, Denise.
Your referral means a lot to me. I’ve really enjoyed your comments on the geometry problem. I’m convinced that our children, our students, all of us can benefit from taking the time to ‘play math’ like you’ve been doing. Cliches like ‘less is more’ and ‘keep it simple, ———‘ are usually on target. Sometimes the simplest questions can lead to the most profound ideas. This is why Liping Ma wrote about American children needing a more ‘profound understanding of fundamental mathematics.’ Good luck with all you’re doing.
Dave Marain
MathNotations

Very nice, sarsen56! I will have to remember that construction for the next time my geometry class gets to experiment with compass and straight-edge. After the more serious geometry proof work, we always take time to play with designs — and that looks like a fun one.

The Bronze Age lozenge is fun, I won’t give it all away just yet in case one of your students wants to try and resolve it. I will give them one clue; the ziz-zag border motif utilizes the residual ‘marking out’ points of the inner series of concentric smaller lozenges. In fact there are at least two other 4,000 year old British lozenge designs, one is also based on a hexagon, a second on the ingenious use of a decagon. As for the 5,000 year old fifty-six sided polygon, well that’s another story!
AJ

Thought of you when I ran across this site.

Maureen

Thanks, Denise.

Your referral means a lot to me. I’ve really enjoyed your comments on the geometry problem. I’m convinced that our children, our students, all of us can benefit from taking the time to ‘play math’ like you’ve been doing. Cliches like ‘less is more’ and ‘keep it simple, ———‘ are usually on target. Sometimes the simplest questions can lead to the most profound ideas. This is why Liping Ma wrote about American children needing a more ‘profound understanding of fundamental mathematics.’ Good luck with all you’re doing.

Dave Marain

MathNotations

You may like to see some ancient geometry:

http://sarsen56.wordpress.com/solve-this/

Very nice, sarsen56! I will have to remember that construction for the next time my geometry class gets to experiment with compass and straight-edge. After the more serious geometry proof work, we always take time to play with designs — and that looks like a fun one.

Thanks for the comment Denise,

The Bronze Age lozenge is fun, I won’t give it all away just yet in case one of your students wants to try and resolve it. I will give them one clue; the ziz-zag border motif utilizes the residual ‘marking out’ points of the inner series of concentric smaller lozenges. In fact there are at least two other 4,000 year old British lozenge designs, one is also based on a hexagon, a second on the ingenious use of a decagon. As for the 5,000 year old fifty-six sided polygon, well that’s another story!

AJ

In response to quite a few people asking more information – I added the next stage in working out the ancient lozenge design..!