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Dudeney’shaberdasher puzzel<br />
Part 1 Introduction<br /><ul><li>Who was Dudeney ?
Short explanationDudeney’sfamoustpuzzle
An appetizer  Donatus logo dissection + animation
Arrange pieces tocreateanequilateraltriangleand square.</li></li></ul><li>Whowas Dudeney ?<br />Henry Ernest Dudeney (1857...
Dudeney’smost famouspuzzleproblem<br />Cut anequilateraltriangleinto 4 pieces <br />thatcanberearranged<br />To make a qua...
Een appetizer<br /><br />Step 1:Print this logo<br />Step 2:<br />Cut into 4 pieces <br />Step 3:<br />Arrange these piec...
Andconversely…put the pieces togethertot obtain a square<br />
Part 2  “Do the Dudeney !” Search Inquiry…<br /><ul><li>2AFind a construction
Use the Internet
 2B  Make thisconstructionwithGeoGebra</li></li></ul><li>Step by step constructionwithGeoGebra<br /><ul><li>Start GeoGebra...
Draw segment AB length 2
Construct anequilateraltrianglevABC</li></li></ul><li>The side of the square<br /><ul><li>midpointsD fromAC andE fromBC
Perpendicularlinesfrom D and E on segment AB
Intersection points F en G with AB
Draw the segment EF
A (very) goodapproximationfor the length of the side Z of the square is EF</li></li></ul><li>The 4 pieces of the puzzle<br...
Draw a triangleFIG</li></li></ul><li>Hingeddissection (rotations) <br />
Part3  “Calculations<br /><ul><li>Check youranswer
What is wrong ? A mistake ?
A goodapproximations ?
Conclusion …</li></li></ul><li>Calculations<br />Calculate area equilateraltriangle side 2<br />Calculatelenghtconstructed...
1 Area trianglewith side 2 <br />
2. Lengthconstructed side EF<br />
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Dudeney dwi english

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Dudeney’s haberdasher puzzel

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Dudeney dwi english

  1. 1. Dudeney’shaberdasher puzzel<br />
  2. 2. Part 1 Introduction<br /><ul><li>Who was Dudeney ?
  3. 3. Short explanationDudeney’sfamoustpuzzle
  4. 4. An appetizer Donatus logo dissection + animation
  5. 5. Arrange pieces tocreateanequilateraltriangleand square.</li></li></ul><li>Whowas Dudeney ?<br />Henry Ernest Dudeney (1857-1930)<br />English mathematician<br />Inventorsomeparticularlyfamous puzzels<br />Published in a book“Canterbury puzzles” in 1907<br />
  6. 6. Dudeney’smost famouspuzzleproblem<br />Cut anequilateraltriangleinto 4 pieces <br />thatcanberearranged<br />To make a quarewith the same area<br />?<br />
  7. 7. Een appetizer<br /><br />Step 1:Print this logo<br />Step 2:<br />Cut into 4 pieces <br />Step 3:<br />Arrange these pieces sothatyouobtainanequilateraltriangle<br /><br /><br />
  8. 8. Andconversely…put the pieces togethertot obtain a square<br />
  9. 9. Part 2 “Do the Dudeney !” Search Inquiry…<br /><ul><li>2AFind a construction
  10. 10. Use the Internet
  11. 11. 2B Make thisconstructionwithGeoGebra</li></li></ul><li>Step by step constructionwithGeoGebra<br /><ul><li>Start GeoGebra online link or installGeoGebra on your computer download
  12. 12. Draw segment AB length 2
  13. 13. Construct anequilateraltrianglevABC</li></li></ul><li>The side of the square<br /><ul><li>midpointsD fromAC andE fromBC
  14. 14. Perpendicularlinesfrom D and E on segment AB
  15. 15. Intersection points F en G with AB
  16. 16. Draw the segment EF
  17. 17. A (very) goodapproximationfor the length of the side Z of the square is EF</li></li></ul><li>The 4 pieces of the puzzle<br /><ul><li>Draw 3 polygons AFHD HDCE EIGB
  18. 18. Draw a triangleFIG</li></li></ul><li>Hingeddissection (rotations) <br />
  19. 19. Part3 “Calculations<br /><ul><li>Check youranswer
  20. 20. What is wrong ? A mistake ?
  21. 21. A goodapproximations ?
  22. 22. Conclusion …</li></li></ul><li>Calculations<br />Calculate area equilateraltriangle side 2<br />Calculatelenghtconstructed side EF<br />Area square = Area triangle<br />Calculate exact lenght side Z square<br />ComparelengthEF with exact lengthZ<br />Conclusion… ?<br />
  23. 23. 1 Area trianglewith side 2 <br />
  24. 24. 2. Lengthconstructed side EF<br />
  25. 25. 3. Area square = area triangle<br />4. Calculation exact length side Z for square ?<br />
  26. 26. 4. ComparelengthEF with exact valueZ<br />This “simple” constructionis a verygoodAPPROXIMATION because …<br />
  27. 27. 5. Controle van gevonden resultaten<br />Area square approximated<br />Area square exact<br />
  28. 28. Conclusion<br />Approximatedvalueside Z (EF)<br />Exact value<br />
  29. 29. There is a small differencebetweenthe exact length Z of the square and the length of EF (construction) <br />
  30. 30. <ul><li>The exact construction
  31. 31. GeoGebra
  32. 32. Exact calculations
  33. 33. Animationhingedpuzzle</li></ul>Part 4 Follow up<br />
  34. 34. A real challenge!<br />The originalbookDudeney’s “Canterbury puzzles” ONLY a picture for theexact constructionNO EXPLANATION !!!<br />Theproblemis to construct …<br />
  35. 35. PART 5 ProofwithGeoGebra<br />
  36. 36. Part 6 AnimationGeoGebra<br />Meer info ivan.dewinne@telenet.be<br />Website www.mathelo.be<br />

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