2004-05-25 news articles on origami:   BostonGlobe and CNN.



Shukong Ou <email: shukong@ourigami.com>

<fax & voicemail: 978-477-0074>



Friday, May 14th,  2004, at St John’s Preparatory School, Danvers, MA

A Talk about Geometry and Origami



What is Geometry ?




 Let’s look at a Circle


Geometry is “looking in one of the windows at the House of Mathematics”.  The other windows may be algebra, trigonometry, calculus, differential equations, …  What are some other windows in this house ?


This simple shape can be viewed in many different ways

1)      in geometry, we can construct a circle with a compass (point and pencil)

2)      in algebra, x2 + y2 = 0, or  (r=1, θ) in Polar Coordinates

3)      astronomy, orbits of moons, planets, comets, stars (not quite circles, are they?)

4)      ripples on a pond

5)      {cone ∩ “plane ┴ axis of symmetry of cone” }

What other circle-views can you think of ?



Geometry & origami







Traditional Geometry à


Origami à


Geometry is naturally an intimately related to origami –

1)      folding à 3 dimensional result (make a cone !)

2)      edges of paper à represent lines & “constructions

3)      folds easily establish straight lines

4)      things are more fun in 3 dimensions

What are some other ways where origami and geometry are related ?


Requires 3 tools:  straightedge, compass, protractor


Requires just the paper (none of the traditional tools)

2 folds to construct a common angle – (demonstration)

Fold a piece of paper so X-axis motion (side /side) causes Y-axis motion (up /down)



Three Impossible Things

(before breakfast)


1)      A piece of paper can have one side.

2)      Fold a piece of paper so X-axis motion (side /side) causes motion in a perpendicular direction, Y-axis (up /down)

3)      2 π R = 2 π r   …and…   A fancier proof (and a challenge).



Time permitting…

Continue after school ?



Unit origami – repeated “units” to construct “Platonic Solids”

Tetrahedron (4f, triangle), hexahedron (what’s the other name?) (6f, square), octahedron (8f, triangle), dodecahedron (12f, pentagon), icosahedron (20f, triangle).


Units generally have “handedness” – right hand shakes right hand, but right hand does not “fit” left hand.