Preface
Acknowledgements
ch. 1. Hard lines
1.1. Cutting lines
1.2. The Pythagorean theorem
1.3. Broad lines
1.4. Cutting lines
1.5. Trial by trials
ch. 2. How to draw a straight line
2.1. Approximate-straight-line linkages
2.2. Exact-straight-line linkages
2.3. Hart's exact-straight-line mechanism
2.4. Guide linkages
2.5. Other ways to draw a straight line
ch. 3. Four-bar variations
3.1. Making linkages
3.2. The pantograph
3.3. The crossed parallelogram
3.4. Four-bar linkages
3.5. The triple generation theorem
3.6. How to draw a big circle
3.7. Chebyshev's paradoxical mechanism
ch. 4. Building the world's first ruler
4.1. Standards of length
4.2. Dividing the unit by geometry
4.3. Building the world's first ruler
4.4. Ruler markings
4.5. Reading scales accurately
4.6. Similar triangles and the sector
ch. 5. Dividing the circle
5.1. Units of angular measurement
5.2. Constructing base angles via polygons
5.3. Constructing a regular pentagon
5.4. Building the world's first protractor
5.5. Approximately trisecting an angle
5.6. Trisecting an angle by other means
5.7. Trisection of an arbitrary angle
5.8. Origami.

ch. 6. Falling apart
6.1. Adding up sequences of integers
6.2. Duijvestijn's dissection
6.3. Packing
6.4. Plane dissections
6.5. Ripping paper
6.6. A homely dissection
6.7. Something more solid
ch. 7. Follow my leader
ch. 8. In pursuit of coat-hangers
8.1. What is area?
8.2. Practical measurement of areas
8.3. Areas swept out by a line
8.4. The linear planimeter
8.5. The polar planimeter of Amsler
8.6. The hatchet planimeter of Prytz
8.7. The return of the bent coat-hanger
8.8. Other mathematical integrators
ch. 9. All approximations are rational
9.1. Laying pipes under a tiled floor
9.2. Cogs and millwrights
9.3. Cutting a metric screw
9.4. The binary calendar
9.5. The harmonograph
9.6. A little nonsense!
ch. 10. How round is your circle?
10.1. Families of shapes of constant width
10.2. Other shapes of constant width
10.3. Three-dimensional shapes of constant width
10.4. Applications
10.5. Making shapes of constant width
10.6. Roundness
10.7. The British Standard Summit Tests of BS3730
10.8. Three-point tests
10.9. Shapes via an envelope of lines
10.10. Rotors of triangles with rational angles
10.11. Examples of rotors of triangles
10.12. Modern and accurate roundness methods.

ch. 11. Plenty of slide rule
11.1. The logarithmic slide rule
11.2. The invention of slide rules
11.3. Other calculations and scales
11.4. Circular and cylindrical slide rules
11.5. Slide rules for special purposes
11.6. The magnameta oil tonnage calculator
11.7. Non-logarithmic slide rules
11.8. Nomograms
11.9. Oughtred and Delamian's views on education
ch. 12. All a matter of balance
12.1. Stacking up
12.2. The divergence of the harmonic series
12.3. Building the stack of dominos
12.4. The leaning pencil and reaching the stars
12.5. Spiralling out of control
12.6. Escaping from danger
12.7. Leaning both ways!
12.8. Self-righting stacks
12.9. Two-tip polyhedra
12.10. Uni-stable polyhedra
ch. 13. Finding some equilibrium
13.1. Rolling uphill
13.2. Perpendicular rolling discs
13.3. Ellipses
13.4. Slotted ellipses
13.5. The super-egg
Epilogue
References
Index.