2500年以上研究されてきた歴史を持つ「幾何学」と名のつく数学の一部門を取り上げます。幾何学には古代ギリシアで体系化されたユークリッド幾何学をはじめ、近代以後の非ユークリッド幾何学、曲がった空間、ルネサンス芸術における射影幾何学、ブラックホール時空の幾何学など多くの分野があります。基礎からプラトンの立体のような数学的対象、ピタゴラスの定理などの具体例を挙げ、その原則を概説するとともに、広く科学や芸術との関係についても言及します。
 

• Offers a fresh modern introduction to a fundamental branch of mathematics, from Euclid to the geometry of spacetime in black holes
• Stretches the reader but requires no more than high school mathematics
• Highlights the broader connections of geometry with science and art

   
The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose. To this day geometry remains a very active area of research in mathematics.
   
This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Starting from the basics, Maciej Dunajski proceeds from concrete examples (of mathematical objects like Platonic solids, or theorems like the Pythagorean theorem) to general principles. Throughout, he outlines the role geometry plays in the broader context of science and art.