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A Geometric Inspection of Pennsylvanian Dutch Hex Signs

A Geometric Inspection of Pennsylvanian Dutch Hex Signs. Evans Evans. Common Hex Signs. Eight Pointed Star. Common Hex Signs. Double Eagle. Six Petal Rosette. Eight Star. Double Distlefink. Triple Star. Mighty Oak. Single Distlefink. What is a Hex Sign.

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A Geometric Inspection of Pennsylvanian Dutch Hex Signs

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  1. A Geometric Inspection of Pennsylvanian Dutch Hex Signs Evans Evans

  2. Common Hex Signs

  3. Eight Pointed Star

  4. Common Hex Signs Double Eagle Six Petal Rosette Eight Star Double Distlefink Triple Star Mighty Oak Single Distlefink

  5. What is a Hex Sign Bright Colorful Geometric Designs Circular discs painted on barns Star-Polygons, Birds, Tulips, & Hearts

  6. Where are they? “Pennsylvania Dutch Country” Southeastern Pennsylvania Between Philadelphia and Harrisburg

  7. Map of “Dutch Country”

  8. When it all Began 1800’s Region is settled by German immigrants 1850’s Six Petal Rosettes appear 1900’s Birds, Hearts, Tulips appear

  9. How they Do That? Simple Tools Nail, Rope, Straight Edge, Paint Creativity and Ingenuity

  10. Six Petal Rosette A Finite Design has 2 classification: “Cyclic” (cn) or “Dihedral” (dn) Has a d6 Finite Rotational Property

  11. Construction of a Rosette Another Congruent Circle with center at new intersection point Congruent Circle with center at Point B

  12. Double Distlefink pxyz p: pattern x: vertical reflection y: horizontal reflection z: half-turns One Fold Reflection pm11 m1

  13. Triple Star Any {n,k} Star-polygon is made in one stroke NOTE:20 points on Circle 4 pentagonal star-polygons Order: {5,2}

  14. Star-Polygon Pentagonal Star-Polygon {5,2} Divide Circle into 5 equally spaced points Start at point “1” and connect every 2nd point

  15. Construction of the Golden Cut Construct a Perpendicular Line to AB through point B Line Segment AB with Midpoint C Make Circle B with radius BC to find Point D on perpendicular line Golden Ratio : Form Triangle ABD Make Circle A with radius AE to find point G on line segment AB AB = AG AG GB Make Circle D with radius DB to find point E on line AD Phi :

  16. The Golden Cut on a Circle Construct Circle A with radius AG Finish with exactly 10 Circles and 10 equally spaced points around the Center Circle B Make Circle B with radius AB Construct another Circle with radius AG and center at intersection of the 2 Circles Repeat this process around the circumference of the Circle B

  17. 10-20 Congruent Points Continue this process around the entire Circle Bisect Angle 1B2 to get a midpoint on arc of Circle B

  18. Pentagonal Star Polygon

  19. Quad Star Polygon

  20. Shading of the Star

  21. Simple Tools

  22. Maple Leaf Outer Ring has a c1 finite design Inner Ring has a d8 rotational property

  23. Double Trinity Tulip One Fold Reflection m1 Inner Circle has a d6 rotational property

  24. Where can YOU find a connection between MATH and ART? Any Questions?

  25. Thank You A Geometric Inspection of Pennsylvanian Dutch Hex Signs Evan Evans

  26. Rosettes in Egypt Rosettes in Asia Rosette in Ancient Rome

  27. Daddy Hex Outer Ring is a c4’ finite rotation Inner Ring is a d2’ finite rotation

  28. Kissing Circles

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