dudeney dwi english

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

Part 6 Animation GeoGebra

Meer info ivan.dewinne@telenet.be

Website www.mathelo.be