bodner054

After creating the slide togethers by George Hart, I decided that I wanted to create my own models. Here is the Product of My Experimentation    I used cardstock for all of the models. I created a flower blossom slide together with 60 degree angles.  The model was hard to put together because the edges did not line up correctly...maybe it was an angle problem but the interior of the design looks like an equilateral triangle. Oh well, it's a pretty flower and I am posting it for anyone who is interested in a challenge.  But be forewarned, it will collapse while putting together...use glue or paper clips and hold tightly by cupping the model in your hand when constructing the model.  Here is the .Studio file.  Cut 20 shapes for one model or two pages with extra pieces. https://docs.google.com/file/d/0B7oGIyVDbRGYOGxUZFVLel9NUE0/edit?usp=sharing Flower Blossom Slide Together Butterfly slide together with 72 degree angles...notice the pentagon shape insid...

George Hart is my hero.  His website http://www.georgehart.com/ is fabulous.  His objective is to make math cool and I think he achieves this goal. I have designed the cutting files for all seven slide togethers. Please me mindful of George Hart's work. I copied the work to promote his mission of making math cool and help others who want to explore and enjoy his work.  As he says on his website..."the  templates below may be freely copied for educational purposes. Creative teachers can undoubtedly incorporate these constructions into classes of different levels in ways which I would never think of" http://www.georgehart.com/slide-togethers/slide-togethers.html The photographs below have a tape measure in each picture so that you can see the size of each model...just in case you would like to resize. Also, some of the templates maximize the amount of paper if you are cutting this out for a class and have extra pieces. Use cardstock for making...

Challenge: Make a Origami Buckyball ( A dodecahedron -  20 vertices, 30 edges, 12 faces (regular pentagons))  using three colors so that no two units of the same color touch. I love puzzles and this challenge took me a few hours to solve. In order to solve this puzzle, I had to do a little exploration of the materials.  Given three different colors that meet at a point...how many combinations can there be.  As you can see from the photo below, only two. The next problem was combining these pieces to create a pentagon.  How many different combinations are there?  Three combinations. The final problem is how to put these pentagons together to create the dodecahedron, where all vertices are different colors and don't touch one another. After trying a few combinations, I discovered that I needed more theory.  It is a circuit problem.  A Hamilton Circuit in particular. Starting at a point in the middle.  You need to draw a...

The Museum of Mathematics in NYC created this hyperbolic paraboloid sliceform.  It is amazing to see the form take place as you put it together. It lies flat after you put it together! You have to love it! My daughter loved the fact that when the parabola lies flat it shows the integrals for the area under the curve...a good sliceform to show to a calculus class.  For the less mathematical people,  the area under the curve can be explained as...what is the area of this three dimensional parabola?  The area of multiple two dimensional rectangles added together will result in the approximation of the total area of this 3 D parabola. Here is the link to the pdf of this sliceform.  http://momath.org/wp-content/uploads/Hyperbolic_Parabola_Model_85by11.pdf If you have a Cameo Silhouette, you are in luck because I created a .Studio file for this sliceform so you do not have to do any of the cutting by hand. Here are the two .Studio files.  Make one copy of each....

This post might be boring if you don't have a Cameo Silhouette but I am posting it anyway for any math teachers out there that need the cutting file for tangrams.  Tangrams are an excellent activity to give students who have completed their assignments early and are looking for something interesting to do. Here is an excellent PDF worksheet with answers.  The tangram area problem is a nice challenge for geometry students. http://math.schaubroeck.net/files/tangram_ANSWER_KEY.pdf Here is my .Studio file to cut out the tangrams for students. Yes, I know the students can cut them out but as a time saver...you can cut them out ahead of time. https://docs.google.com/file/d/0B7oGIyVDbRGYU05YeXFZbWZlMjg/edit?usp=sharing #tangram #Silhouette

I am working my way through the book entitled "Beginner's Book of Modular Origami Polyhedra: The Platonic Solids".  The book itself has a lot of interesting origami models.  However, the directions are terrible.  The book misnumbers steps, the diagrams do not show which side of the paper to use and it doesn't tell you how much origami paper you need to complete the model. This octahedron was simple to make with six water bomb bases. The pieces slid together in about 20 minutes. I also made this origami gyroscope.  I think it turned out too big.  I used a 4x4 square. Next time, I will be more mindful of the size. Another gripe about this book...they should suggest paper size.  I do like the square cut out in the middle thoug...a window to the other side.

I love sliceforms.  What are they you say?  Well, they are exactly what the term says...slices of a form.  For example, I decided to make a sliceform of a sphere.  I used my designing software with the Cameo Silhouette and created this sphere. I have included the PDF and .Studio files if you would like to make sliceforms at the end of this post. They would look great as a decoration for a party or as an ornament. The shapes took me hours to make so please pass them along and appreciate what math can do!  Marley loves it too! Amazing that it lies flat when put together.   Sliceform Sphere  I saw a sliceform of a torus on the internet.  I made it and then decided it was not pretty enough so I created my own version. The pink torus is the scalloped version and the blue torus is the zigzag version. This time the toruses makes me think of flowers instead of food (a donut).  I love the way the variations of color are created by the shadows of...