SketchUp Geometry Use these fun geometry projects (PDF
format) to challenge your students! Comments or suggestions for future projects? Please email 3DVinci's Bonnie Roskes.

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Three Point Circle January 2012 by Bonnie Roskes This project shows how to create a circle that passes through three points. Using groups makes this project easy. 

Dodecagon from Circle December 2011 by Bonnie Roskes This project shows how to use circles and construction lines to create a dodecagon. You'll also see some ideas for what you can create inside a dodecagon, once've you've created it.
This is a quick and useful project for students of all ages. For older students, The Teacher Version contains the answer to the question at the end of the Student Version, which asks about the number of circle "sides" needed to create the dodecagon. 
Download the Teacher Version (PDF)

Perpendicular Plane November 2011 by Bonnie Roskes This project shows how to start with a line in 3D space, and find its perpendicular plane. This is a great project for all geometry students! 

Pentagon from a Circle May 2011 by Bonnie Roskes This project shows how to start with a circle and create the necessary lines within this circle to construct a pentagon. It's a quick and useful project for middle school or high school geometry students. The Teacher Version contains the answer to the question at the end of the Student Version. 

What is This Solid? April 2011 by Bonnie Roskes This project shows you how to make what's in this video: This project creates a fantastic exercise in 3D thinking for all ages, and it's not hard to do. 

Rhombic Hexacontahedron February 2011 by Bonnie Roskes This stellated solid is comprised of 60 identical rhombic faces. There are a few ways to create it in Google SketchUp, but the method I've used starts with an icosahedron which is used as the basis to create one rhombohedron. Twenty of these rhombohedra are needed, so lots of copies are made. And as an added twist, I've shown how to paint this solid using only 5 colors, so that no color is repeated around any vertex. This project makes use of groups and components, and takes advantage of the rotationaxis setting feature of the Rotate tool. It's one of our more complicated Math Forum projects, so a bit of SketchUp knowledge doesn't hurt! Though detailed steps are provided, so give it a try even if you're a SketchUp newbie. 

Hexagonal Pyramid November 2010 by Bonnie Roskes This looks like a simple project (and it is), but it shows how easily SketchUp can make basic solid objects, and that there's often more than one way to create something in SketchUp. This is a great project for anyone interested in 3D geometry. 

Pentaflake October 2010 by Bonnie Roskes Love fractals? You can create this very cool snowflakelooking model by starting with a simple pentagon. A few SketchUp tools are all you need to complete this project. This is a great project for anyone interested in fractals, or if you just like interesting shapes! 

Esrefoglu Pattern September 2010 by Bonnie Roskes Sorry for the summer hiatus, but we're back with some great projects for the 20102011 school year! No, the name of this project is not a typo. Esrefoglu is the name of a mosque in Turkey, which contains a beautiful geometric pattern based on hexagons. This project shows how to create the hexagon, using some simple SketchUp tools. This hexagon can tile to create some beautiful patterns. This is a great project for anyone interested in periodic patterns. 

Rhombic Dodecahedron May 2010 by Bonnie Roskes The projects from the last few months have been in 2D, so it's time for one in 3D! The name of this 3D solid may sound complicated, but it's actually pretty easy to create in SketchUp. All you need is one square, plus a few simple SketchUp tools. You'll first learn how to create a stellated rhombic dodecahedron: Then learn how to get the rhombic dodecahedron, a 3D solid whose faces are 12 identical rhombi. This is a great project for older students, and younger students will enjoy watching it and of course, coloring it! 

Triangle Medians and Centroid April 2010 by Bonnie Roskes and Jon Choate Every triangle has three medians: lines that start at a corner point and end at the midpoint of the opposite edge. These medians meet at the same point: the centroid. This project will show how to create the medians, and you'll explore some of the length and area relationships within the triangle. This is an easy and interesting 2D geometry project for any age.
Older students who can delve into vector geometry can try this proof: why is each median divided at the centroid into two segments which always have a 2:1 length ratio? 

Isosceles Triangles Form a Square March 2010 by Bonnie Roskes
I got the idea for this project from
a video I
found on the website
of Bill Lombard, a high school math teacher and writer of
math education resources. He shows how you can assemble seven
right isosceles triangles to form a square. (The number doesn't have to be
seven; there are a few ways you can arrange the triangles.)
This is a fun and easy project in SketchUp  you can start with a single line, use it to form a triangle, and use new edges to build increasingly larger triangles. You'll also explore the relationships between areas and edge lengths of neighboring triangles. 

Girih Tiles February 2010 by Bonnie Roskes
Girih tiles
are a
set of five tiles used to create beautiful and intricate patterns,
most commonly seen in Islamic architecture. In this project, you'll learn
about these tiles and see how they can be combined into fanstastic
patterns.


Conic Sections January 2010 by Bonnie Roskes
In this project, you'll build a cone, then use SketchUp's Section
Plane tool to create four different conic curves: circle, ellipse, hyperbola,
and parabola. More advanced students can also check their results based on equations of the
curves.


Building Perspectives: Logical Thinking December 2009 by Bonnie Roskes For this interesting project, all you need is SketchUp and a projector. The idea is to start with a grid of "buildings" and show your students only specific views of them (front, left, right, or back). Students make observations about which buildings are in front of or behind other buildings, and figure out which buildings have which height.
This is a great project for students in middle school and higher. Older students can try it out with larger and larger grids. 

Symmetry and Fall Leaves November 2009 by Bonnie Roskes In this
project, you'll start
with a digital photo of a leaf, and trace around half of it
in SketchUp. You'll use mirror symmetry to see how close the leaf is to
truly symmetric. More advanced students can also use rotational symmetry to make a
wreath.
Students in middle school and high school can do this project on their own, and younger students will enjoy watching a teacher demonstrate it. Not only is this a great math project, the concepts are also valuable for students in art and biology classes. 

Escher Square Tiles October 2009 by Bonnie Roskes and Jon Choate In this
project, you'll start with a square, and use simple tools like Line and
Move to transfom the square into an Escher tile, decorated using your
own creativity. You'll also see how to create tiles from rectangles and
rhombii.
Recommended for Grade 3 and up, this project will appeal not only to geometry students, but also to students interested in art or graphic design. 

September 2009 by Bonnie Roskes and Jon Choate In
this project, you'll create a cube by assembling smaller cubes, then paint
the outside faces of each small cube. For a 2 x 2 x 2 cube, how
many cubes will have three faces painted? Two faces? One face? Zero faces?
What happens when you build larger cubes: 3 x 3 x 3, Recommended for Grade 8 and up, this project will get students to think and visualize objects in 3D, and will help them find patterns in tables of numbers. 
