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Dudeney’s haberdasher puzzelTRANSCRIPT
Dudeney’s haberdasher puzzel
Part 1 Introduction• Who was Dudeney ?
• Short explanation Dudeney’s famoust puzzle
• An appetizer Donatus logo dissection + animation
• Arrange pieces to create an equilateral triangle and square.
Henry Ernest Dudeney (1857-1930)
English mathematician
Inventor some particularly famous puzzels
Published in a book “Canterbury puzzles” in 1907
Who was Dudeney ?
Dudeney’s most famous puzzle problem
Cut an equilateral triangle into 4 pieces
that can be rearranged
To make a quare with the same area
?
Een appetizerStep 1:
Print this logo
Step 2:
Cut into 4 pieces
Step 3:
Arrange these pieces so thatyou obtain an equilateral triangle
And conversely…put the pieces together
tot obtain a square
Part 2 “Do the Dudeney !”
Search Inquiry…
2A Find a construction
Use the Internet
2B Make this construction with GeoGebra
Step by step construction with GeoGebra
Start GeoGebra online link or install GeoGebra on your computer download
Draw segment AB length 2
Construct an equilateral trianglev ABC
The side of the square
midpoints D from AC and E from BC
Perpendicular lines from D and E on segment AB
Intersection points F en G with AB
Draw the segment EF
A (very) good approximation for the length of the side Z of the square is EF
The 4 pieces of the puzzle
Draw 3 polygons
AFHD HDCE EIGB
Draw a triangle FIG
Hinged dissection (rotations)
Check your answer
What is wrong ? A mistake ?
A good approximations ?
Conclusion …
Part 3 “Calculations
Calculations
1. Calculate area equilateral triangle side 2
2. Calculate lenght constructed side EF
3. Area square = Area triangle
4. Calculate exact lenght side Z square
5. Compare length EF with exact length Z
6. Conclusion … ?
1 Area triangle with side 2
2. Length constructed side EF
3. Area square = area triangle
Z ?4. Calculation exact length side Z for square ?
4Z 3
4. Compare length EF with exact value Z
4Z 37 7EF=
4 2
This “simple” construction is a very goodAPPROXIMATION
because …
5. Controle van gevonden resultaten
Area square approximated
2 27 7(EF) =( )
4 4
Area square exact
2 24Z ( 3) 3
ConclusionApproximated value
side Z (EF)
Exact value
71,75
4
3 1,732050808...
73
4
1,75 1,732050808...
There is a small difference between the exact length Z of the square
and the length of EF (construction)
The exact construction
GeoGebra
Exact calculations
Animation hinged puzzle
Part 4 Follow up
A real challenge !The original book Dudeney’s “Canterbury puzzles” ONLY a picture for the exact constructionNO EXPLANATION !!!
4Z 3
The problem is to construct …
PART 5 Proof with GeoGebra
