Do Bees Build It Best? - PowerPoint PPT Presentation

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Do Bees Build It Best?

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  1. Do Bees Build It Best? Geometry Trigonometry

  2. BUILDING THE BEST

  3. NAILING DOWN AREA

  4. HOW MANY CAN YOU FIND?

  5. THAT’S ALL THERE IS!

  6. HALVING YOUR WAY

  7. PARALLELOGRAMS AND TRAPEZOIDS

  8. FORMING FORMULAS

  9. GOING INTO THE GALLERY

  10. A RIGHT-TRIANGLE PAINTING

  11. A TRIGONOMETRIC SUMMARY

  12. MORE GALLERY MEASUREMENTS

  13. A HOMEMADE TRIG TABLE

  14. SHADOWS AND SAILBOATS

  15. TRI-SQUARE RUG GAMES

  16. ANY TWO SIDES WORK • LEG^2 + LEG^2 = HYP^2

  17. IMPOSSIBLE RUGS

  18. MAKE THE LINES COUNT

  19. PROOF BY RUGS

  20. THE POWER OF PYTHAGORAS

  21. LESLIE’S FERTILE FLOWERS

  22. FLOWERS FROM DIFFERENT SIDES

  23. DON’T FENCE ME IN

  24. RECTANGLES ARE BORING!

  25. MORE FENCING, BIGGER CORRALS

  26. MORE OPINIONS ABOUT CORRALS

  27. BUILDING THE BEST FENCE

  28. FALLING BRIDGES

  29. LESLIE’S FLORAL ANGLES

  30. FLAT CUBES

  31. FLAT BOXES

  32. A VOLUMINOUS TASK

  33. PUT YOUR FIST INTO IT

  34. THE INS AND OUTS OF BOXES

  35. A SCULPTURE GARDEN

  36. THE WORLD OF PRISMS

  37. SHEDDING LIGHT ON PRISMS

  38. PYTHAGORAS AND THE BOX

  39. BACK ON THE FARM

  40. WHICH HOLDS MORE?

  41. CEREAL BOX SIZES

  42. A-TESSELLATING WE GO

  43. A PORTFOLIO OF FORMULAS

  44. THAT’S ALL THERE IS! • EACH TRIANGLE MUST HAVE AN AREA OF 2 UNITS • EACH TRIANGLE MUST HAVE ITS VERTICES ON PEGS • EACH TRIANGLE MUST HAVE A HORIZONTAL SIDE

  45. HALVING YOUR WAY

  46. FORMING FORMULAS • LOOK FOR WAYS TO CUT UP THE PARALLELOGRAMS AND TRAPEZOIDS INTO TRIANGLES

  47. GOING INTO THE GALLERY • REMEMBER, THE HEIGHT IS ALSO THE ALTITUDE WHICH IS DRAWN PERPENDICULAR TO THE BASE

  48. A RIGHT-TRIANGLE PAINTING • DRAW A RIGHT TRIANGLE THAT HAS A 55 DEGREE ANGLE • EXTEND BOTH SIDES SO THAT THEY ARE AT LEAST 10 CM IN LENGTH

  49. A TRIGONOMETRIC SUMMARY • SIN A = OPPOSITE/HYPOTENUSE • COS A = ADJACENT/HYPOTENUSE • TAN A = OPPOSITE/ADJACENT

  50. A HOMEMADE TRIG TABLE • DRAW A RIGHT TRIANGLE USING THE ASSIGNED ANGLE FOR YOUR GROUP • MEASURE ALL THE SIDES • COMPUTE THE RATIOS OF SIN, COS, AND TAN