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This small book, now translated into English, is a unique place to find classical results from geometry. The selection of topics is intelligent, varied, and stimulating. In a small space the author provides many thought-provoking ideas.
Oene Bottema (1901-1992) may not be so well known abroad, but in his own country he is "the great geometer". He graduated from the University of Groningen in 1924 and obtained his doctor's degree from Leiden University in 1927. He spent his early years as a high school teacher and administrator. He published extensively, and as his ability became known, he was made professor at the Technical University of Delft in 1941, and later rector of thatuniversity(1951-1959). Withhisencyclopedicknowledgeof19th-century geometry and his training in 20th-century rigor, he was able to make many contributions to elementary geometry, even as that subject was eclipsed by the modern emphasis on abstract mathematical structures. He also had a fruitful collaboration with engineers and made substantial contributions to kinematics, culminating in the book Theoretical Kinematics,withBernard Roth, in 1979. Throughout his life he was inspired by geometry and poetry, and favored elegant succinct proofs. This little book, ?rst published in 1944,then in a secondexpanded edition in 1987, gives us a glimpse into his way of thinking. It is a series of vignettes, each crafted with elegance and economy. See, for example, his proof of the Pythagorean theorem (1. 2), which requires only one additional line to be drawn. And who can imagine a simpler proof of the nine-point circle (4. 1)? There is ample coverage of the modern geometry of the triangle: the Simson line, Morley's theorem, isogonal conjugates, the symmedian point, and so forth.
Oene Bottema (1901-1992) may not be so well known abroad, but in his own country he is "the great geometer". He graduated from the University of Groningen in 1924 and obtained his doctor's degree from Leiden University in 1927. He spent his early years as a high school teacher and administrator. He published extensively, and as his ability became known, he was made professor at the Technical University of Delft in 1941, and later rector of thatuniversity(1951-1959). Withhisencyclopedicknowledgeof19th-century geometry and his training in 20th-century rigor, he was able to make many contributions to elementary geometry, even as that subject was eclipsed by the modern emphasis on abstract mathematical structures. He also had a fruitful collaboration with engineers and made substantial contributions to kinematics, culminating in the book Theoretical Kinematics,withBernard Roth, in 1979. Throughout his life he was inspired by geometry and poetry, and favored elegant succinct proofs. This little book, ?rst published in 1944,then in a secondexpanded edition in 1987, gives us a glimpse into his way of thinking. It is a series of vignettes, each crafted with elegance and economy. See, for example, his proof of the Pythagorean theorem (1. 2), which requires only one additional line to be drawn. And who can imagine a simpler proof of the nine-point circle (4. 1)? There is ample coverage of the modern geometry of the triangle: the Simson line, Morley's theorem, isogonal conjugates, the symmedian point, and so forth.
From the reviews of the second edition:
"This small book includes Ceva's and Menelaus's theorems, the nine-point circle and Euler line, configuration theorems, Morley's triangle, inequalities for elements in a triangle ... . The arguments are not only geometric or trigonometric ones but also different coordinate systems are considered such as barycentric or trilinear coordinates in relation to a given triangle. ... The book is very useful for teachers and teacher students who want to be inspired by the results of elementary geometry." (Herbert Hotje, Zentralblatt MATH, Vol. 1159, 2009)
"This small book includes Ceva's and Menelaus's theorems, the nine-point circle and Euler line, configuration theorems, Morley's triangle, inequalities for elements in a triangle ... . The arguments are not only geometric or trigonometric ones but also different coordinate systems are considered such as barycentric or trilinear coordinates in relation to a given triangle. ... The book is very useful for teachers and teacher students who want to be inspired by the results of elementary geometry." (Herbert Hotje, Zentralblatt MATH, Vol. 1159, 2009)