## Creative MathematicsProfessor H. S. Wall (1902-1971) developed Creative Mathematics over a period of many years of working with students at the University of Texas, Austin. His aim was to lead students to develop their mathematical abilities, to help them learn the art of mathematics, and to teach them to create mathematical ideas. This book, according to Wall, 'is not a compendium of mathematical facts and inventions to be read over as a connoisseur of art looks over paintings. It is, instead, a sketchbook in which readers try their hands at mathematical discovery.' In less than two hundred pages, he takes the reader on a stimulating tour starting with numbers, and then moving on to simple graphs, the integral, simple surfaces, successive approximations, linear spaces of simple graphs, and concluding with mechanical systems. The book is self contained, and assumes little formal mathematical background on the part of the reader. |

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### Contents

Numbers | 1 |

Ordered Number Pairs | 11 |

Slope | 23 |

Combinations of Simple Graphs | 31 |

Theorems about Simple Graphs | 37 |

The Simple Graphs of Trigonometry | 43 |

The Integral | 55 |

Computation Formulas Obtained by Means of the Integral | 67 |

Simple Surfaces | 93 |

Successive Approximations | 119 |

Linear Spaces of Simple Graphs | 135 |

More about Linear Spaces | 161 |

Mechanical Systems | 175 |

Integral Tables | 187 |

189 | |

Glossary of Definitions | 191 |

### Common terms and phrases

3-space ab;cd abscissa antiderivative Axiom belongs bounded variation called centroid collection of nonoverlapping containing the point Corollary counting number Definition denotes the simple Exercise exists a finite exists a number exists a positive exists a simple f has slope f has X-projection Figure finite collection formulas g-length gradient graph g graph whose X-projection graph with X-projection horizontal line inner product space inner sum largest number least number less line of slope linear space linear transformation nondecreasing nonoverlapping intervals filling number distinct number sequence number set number x ordered number pair ordered pair ordinate outer sum point means point of f point set positive integer positive number Problem proper function proper value rectangular interval rectangular segment respect to g Show simple graph simple kernel simple surface subset Suppose f Theorem vertical lines X-projection the interval