I've currently moved over to blogging at http://mathcraft.wonderhowto.com/
Here I will be posting about 4 times per week and will have a project every week with more in depth information and a how to component and templates. There will also be a user forum for people to submit pictures and ideas.
Thanks! I hope to see you there!
Standardized Testing And Reporting
It's the middle of April and this next week all students at University Preparatory School, where I teach, will be taking the California standardized tests. So I decided to design and build a sculpture that I'm calling "Standardized Testing And Reporting" or "STAR", which is what the California testing program is named. The sculpture is made up of 80 pencils and is held together with a variety of glues.
From the side:
Two of the five identical pieces it is made from:
The sculpture is made from 5 pieces, each of which is part of a hyperbolic paraboloid embedded in a regular tetrahedron. This works because the dihedral angle (angle between faces) of a tetrahedron is 70.5 degrees which when multiplied by 5 (the number of pieces) very nearly results in 360 degrees.
The first inspiration for this work was George Hart's 72 Pencils. This gave me the idea for using Pencils. Here's my recreation of that work:
The second was Carlo H. SÃ©quin's Ribbed Hemicube. This brought the realization that you could easily embed hyperbolic paraboloids into regular tetrahedra. Here's my recreation of that work:
The third was Erik Demaine's Polyhedra built from Hypars (Sections of Hyperbolic Paraboloids). This inspired me to create a full polyhedral structure from sections. (Note: While this looks nearly identical to what I built there are major advantages to working with these folded paper structures. You can make the angles most anything you want. For instance a 6 pointed star would work just as easily) I haven't actually completed one of his works. I'm working on it but I'm a slow folder. Here's a picture from his site:
Here's a few pictures from the build process:
Marking up the pencils so they can be glued in the proper positions:
Getting the Tetrahedral frame together:
The completed tetrahedral frame (The front pencil will be removed):
Starting the hyperbolic paraboloid by connecting pencils across the marks:
One done! (With overlap):
From the side:
Three together (testing the fit)
Five together (Still need to trim off the extra length of the pencils):
After trimming:
The completed sculpture:
Subscribe to:
Post Comments (Atom)
Popular Posts

I've been a big fan of M.C. Escher's Art since I was a little kid. His impossible figures drawings are mindblowing and his tesselat...

This post is going to be on 3D fractals cut on a scroll saw. (Thus the title of course.) As some of you know, I'm somewhat addicted to...

It's the middle of April and this next week all students at University Preparatory School , where I teach, will be taking the California...

I've always been interested in maps and different projections and how they make such a difference in the way the world looks when a sphe...

I ran across an article a couple of months ago talking about an artist making cityscapes using staples to build the buildings. The cities w...

A couple of weeks ago, I suddenly had the idea to make the Platonic solid s out of pennies. I'd made them before out of paper in severa...

I've been a big fan of George Hart's geometric sculptures for a while now and so a few weeks back I decided I would build his Frabjo...

I finally finished a papercraft project I've been working on for about a month. It's made up of parts of 29 sheets of cardstock. I...

I spent a little bit of time on the wooden orrery today. Click here for the original post and description . Two more sets of Gears are done...

This post combines two of my hobbies, making things out of paper (papercrafting) and exploring and building fractals. For those of you that...
7 comments:
That's awesome! And I love your explanation of how you got the idea.
This is a great Math Club project. What did you use to trim the pencils?
I used a dremel with a cutoff disc. Works pretty well. You have to be careful and a couple will probably get detached as a result and have to be reglued.
The only difficulty I ever had was attachment for the pencils. The paint on the pencils doesn't seem to work with very many adhesives...superglue works but not well. The only thing that really worked well was hotglue but it's pretty messy. If I were to do it again I would spend a little while trying to find a better attachment method.
I bet small glue dots would be a great hot glue substitute.
I think I am going to get metal rods and build this out of metal! Way cool!
Can someone please walk me through the steps of making this? It is an extra credit project and it looks really complicated.
Don't like the Dixon pencil structure. I like the Dixon
pencil, but not the idea of a structure with them.
Blackwing pencils are cool.
Post a Comment