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
Cut an equilateral triangle into 4 pieces
that can be rearranged
To make a quare with the same area
?
Step 1:
Print this logo
Step 2:
Cut into 4 pieces
Step 3:
Arrange these pieces so that
you 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
 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
 Draw 3 polygons
AFHD
HDCE
EIGB
 Draw a triangle FIG
Part 3 “Calculations
Check your answer
What is wrong ? A mistake ?
A good approximations ?
Conclusion …
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 … ?
2. Length constructed side EF
3. Area square = area triangle
Z?
4. Calculation exact length side Z for square ?
Z 3
4
4. Compare length EF with exact value Z
7
7
EF=

4
2
Z 3
4
This “simple” construction is a very good
APPROXIMATION
because …
5. Controle van gevonden resultaten
Area square approximated
7 2 7
(EF) =( ) 
4
4
2
Area square exact
Z  ( 3)  3
2
4
2
Approximated value
side Z (EF)
7
 1, 75
4
Exact value
3  1,732050808...
7
 3
4
1,75  1,732050808...

The exact construction



GeoGebra
Exact calculations
Animation hinged puzzle
The original book Dudeney’s “Canterbury puzzles”
ONLY a picture for the exact construction
NO EXPLANATION !!!
The problem is to construct …
Z 3
4
Meer info [email protected]
Website www.mathelo.be