Reality and Imagination
On Problems
Part One: Size and Shape
In which we begin our investigation of abstract geometrical figures.
Symmetrical tiling and angle measurement.
Scaling and proportion.
Length, area, and volume.
The method of exhaustion and its consequences.
Polygons and trigonometry.
Conic sections and projective geometry.
Mechanical curves.
Part Two: Time and Space
Containing some thoughts on mathematical motion.
Coordinate systems and dimension.
Motion as a numerical relationship.
Vector representation and mechanical relativity.
The measurement of velocity.
The differential calculus and its myriad uses.
Some final words of encouragement to the reader.
Acknowledgments
Index
· · · · · · (收起)
On Problems
Part One: Size and Shape
In which we begin our investigation of abstract geometrical figures.
Symmetrical tiling and angle measurement.
Scaling and proportion.
Length, area, and volume.
The method of exhaustion and its consequences.
Polygons and trigonometry.
Conic sections and projective geometry.
Mechanical curves.
Part Two: Time and Space
Containing some thoughts on mathematical motion.
Coordinate systems and dimension.
Motion as a numerical relationship.
Vector representation and mechanical relativity.
The measurement of velocity.
The differential calculus and its myriad uses.
Some final words of encouragement to the reader.
Acknowledgments
Index
· · · · · · (收起)
具体描述
Lockhart's 'Mathematician's Lament' outlined how we introduce mathematics to students in the wrong way. This book explains how mathematics should be done. With plain English and pictures, he makes complex ideas about shape and motion intuitive and graspable, and offers a solution to mathematic phobia.
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