Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Upcoming SlideShare
×

# Dudeney dwi english

1,089 views

Published on

Dudeney’s haberdasher puzzel

Published in: Technology, Education
• Full Name
Comment goes here.

Are you sure you want to Yes No
Your message goes here
• Be the first to comment

### 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 />