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SHADOWS

SHADOWS. SIMILARITY PROPORTIONS TRIGONOMETRY. HOW LONG IS A SHADOW?. EXPERIMENTING WITH SHADOWS. SHADOW DATA GATHERING. LOOKING FOR EQUATIONS. AN N-BY-N WINDOW. MORE ABOUT WINDOWS. DRAW THE SAME SHAPE. HOW TO SHRINK IT?. THE STATUE OF LIBERTY. MAKE IT SIMILAR.

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SHADOWS

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  1. SHADOWS SIMILARITY PROPORTIONS TRIGONOMETRY

  2. HOW LONG IS A SHADOW?

  3. EXPERIMENTING WITH SHADOWS

  4. SHADOW DATA GATHERING

  5. LOOKING FOR EQUATIONS

  6. AN N-BY-N WINDOW

  7. MORE ABOUT WINDOWS

  8. DRAW THE SAME SHAPE

  9. HOW TO SHRINK IT?

  10. THE STATUE OF LIBERTY

  11. MAKE IT SIMILAR

  12. IS THERE A COUNTEREXAMPLE?

  13. TRIANGULAR COUNTEREXAMPLES

  14. WHY ARE TRIANGLES SPECIAL?

  15. ARE ANGLES ENOUGH?

  16. WHATS POSSIBLE?

  17. SIMILAR PROBLEMS

  18. VERY SPECIAL TRIANGLES

  19. INVENTING RULES

  20. WHAT’S THE ANGLE?

  21. MORE ABOUT ANGLES

  22. INSIDE SIMILARITY

  23. A PARALLEL PROOF

  24. INS AND OUTS OF PROPORTION

  25. BOUNCING LIGHT

  26. NOW YOU SEE IT, NOW YOU DON’T

  27. MIRROR MAGIC

  28. MIRROR MADNESS

  29. TO MEASURE A TREE

  30. A SHADOW OF A DOUBT

  31. MORE TRIANGLES FOR SHADOWS

  32. THE RETURN OF THE TREE

  33. RIGHT TRIANGLE RATIOS

  34. REFERENCE: SIN, COS, AND TAN...

  35. YOUR OPPOSITE IS MY ADJACENT

  36. THE TREE AND THE PENDULUM

  37. SMOKEY AND THE DUDE

  38. THE SUN SHADOW PROBLEM

  39. THE SUN SHADOW

  40. BEGINNING PORTFOLIO SELECTION

  41. HOW LONG IS A SHADOW? • THINK OF VARIABLES THAT WOULD AFFECT THE LENGTH OF A SHADOW • MAKE A LIST

  42. HOW LONG IS A SHADOW? • IN YOUR GROUP, CHOOSE ONE VARIABLE TO EXPERIMENT WITH AT HOME • KEEP EVERYTHING ELSE CONSTANT

  43. EXPERIMENTING WITH SHADOWS • EXPERIMENT AT HOME • DESCRIBE RESULTS • INCLUDE NUMERCIAL DATA • DIAGRAM

  44. SHADOW DATA GATHERING • THE HEIGHT OF THE LIGHT SOURCE • THE DISTANCE FROM THE OBJECT TO THE LIGTH SOURCE • THE HEIGHT OF THE OBJECT

  45. SHADOW DATA GATHERING • WHAT FORMULA CAN BE USED TO EXPRESS S AS A FUNCTION OF THE VARIABLES L, D, AND H? S = f(L, D, H)

  46. AN N-BY-N WINDOW • FIND A FORMULA FOR THE TOTAL NUMBER OF WOOD STICKS NEEDED TO BUILD ANY SQUARE WINDOW

  47. LOOKING FOR EQUATIONS • MAKE IN OUT TABLES OF YOUR GROUPS DATA AND 3 OTHER GROUPS • TRY GRAPHING DATA • FIND AN EQUATION

  48. MORE ABOUT WINDOWS • FIND A FORMULA FOR THE TOTAL NUMBER OF WOODEN STICKS NEEDED FOR ANY RECTANGULAR WINDOW M X N WINDOW

  49. HOW TO SHRINK IT? • LOLA’S: KEEP ANGLES THE SAME AND SUBTRACT 5 FROM EACH SIDE • LILY’S : KEEP ALL LENGTHS THE SAME AND DIVIDE THE ANGLES BY 2 • LULU’S : KEEP ALL THE ANGLES THE SAME AND DIVIDE THE LENGHTS OF THE SIDES BY 2

  50. THE STATUE OF LIBERTY’S NOSE • COMPARE YOUR NOSE AND ARM TO THE STATUE OF LIBERTY’S NOSE AND ARM • COMPARE YOUR LEG TO THE STATUE OF LIBERTY’S.

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