Geometrical Aspects of Folding, Origami What geometry terms or ...

Geometrical Aspects of Folding, OrigamiWhat geometry terms or examples did you notice while folding?point: “a specific location” (no length or width, dimension zero)line: “an unending length”, a breadthless length (Euclid), a widthless lengthAfter Euclid’s work had been studied and analyzed, mathematicians decided it isimpossible to define all terms without resorting to infinite regress. Point and line areconsidered to be officially not defined, just undefined words used without definition.The basic building blocks. You need to start somewhere.angles: right (90 degrees), acute (less than 90 degrees), obtuse (90 to 180 degrees), 45degreesparallel lines have equal distance between them, will never intersectperpendicular lines form equal angles (90 degree right angles)square: 4 equal sides and 4 right angles)rectangle: opposite sides are equal and 4 right angles – note all 4 sides do not need to beequal lengthparallelogram: opposite sides equal length and opposite angles are equal – note that all 4angles do not need to be equal. A rectangle that gets pushed over to the side is aparallelogram.Every square is a rectangle. True or False: If it is a square, then it is a rectangle. (True)Not every rectangle is a square. True or False: If it is a rectangle, then it is a square.(False)rhombus: 4 equal sides and opposite angles are equal – note that all 4 angles do not needto be equal. If you take a square and push it over, then you have a rhombus.quadrilateral: any 4 sided polygontriangle: any 3 sided polygonequilateral triangle: 3 sides of equal lengthisosceles triangle: 2 sides of equal lengthscalene triangle: no sides of equal length(over)

Motions:Flip or Reflect (pick up off table and turn over)Rotate (keep flat on the table and turn like the hands of a clockConvex: Fold edges “up”. The fold is away from you, and edges are toward you. AuthorPaul Jackson calls this a valley fold.)Concave: Fold edges “back”. The fold comes toward you, and you move the edges ofthe paper away from you. Author Paul Jackson calls this a mountain fold.Line of Symmetry: both parts look identical on either side of this lineHow to make a square piece of paper by folding:Method 1: Fold one corner down (keep edges even) until you have two isosceles 45-45-90 triangles on top of each other sharing the diagonal hypotenuse. Cut or nail crease andgently tear off the extra strip.orMethod 2: Use a second piece of paper to mark the short side along the length of the longside. Crease. Cut or remove extra strip.