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Summary
Summary
For two millennia the right way to teach geometry was the Euclidean approach, and in many respects, this is still the case. But in the 1950s the cry "Down with triangles!" was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new right approach? Or was the right approach still something else, perhaps transformation groups?
The Four Pillars of Geometry approaches geometry in four different ways, spending two chapters on each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective geometry, and how the hyperbolic plane emerges from the real projective line.
The author begins with Euclid-style construction and axiomatics, then proceeds to linear algebra when it becomes convenient to replace tortuous arguments with simple calculations. Next, he uses projective geometry to explain why objects look the way they do, as well as to explain why geometry is entangled with algebra. And lastly, the author introduces transformation groups---not only to clarify the differences between geometries, but also to exhibit geometries that are unexpectedly the same.
All readers are sure to find something new in this attractive text, which is abundantly supplemented with figures and exercises. This book will be useful for an undergraduate geometry course, a capstone course, or a course aimed at future high school teachers.
John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).
Summary
Kahlil Gibran, author of "The Prophet", is known throughout the world as the immortal Prophet of Lebanon and the Savant of his Age. "A Treasury of Kahlil Gibran", which sold over a hundred thousand copies, led to a wide demand for a sequel volume. The demand has been met in "A Second Treasury of Kahlil Gibran".
In this magnificent volume Gibran's writing in his beloved mother tongue, Arabic, have been translated superbly into Englis by his great friend, Anthony Rizeallah Ferris. Included are four great books: "The Broken Wings", an exquisitely tender, poetic love story; "The Voice of the Master", Gibran's remarkable study of his life; "Thoughts and Meditations", containing Gibran's spiritual message to the world; and "Kahlil Gibran: A Self Portrait", in which Gibran's greatness is revealed through his letters.
Author Notes
Khalil Gibran, also known as Kahlil Gibran, was born on January 6, 1883 in Northern Lebanon. As a result of his family's poverty, he received no formal education as a small child but had regular visits from the local priest who taught him about the Bible as well as the Syrian and Arabic languages. After his father was imprisoned for embezzlement and his family's property was confiscated by the authorities, his mother decided to emigrate to the United States in 1895. They settled in Boston's South End.
He attended public school and art school, where he was introduced to the artist, photographer, and publisher Fred Holland Day. A publisher used some of Gibran's drawings for book covers in 1898. His family forced him to return to Lebanon to complete his education and learn the Arabic language. He enrolled in Madrasat-al-Hikmah, a Maronite-founded school, which offered a nationalistic curriculum partial to church writings, history and liturgy. He learned Arabic, French, and exceled in poetry. He returned to the United States in 1902.
In 1904, he hosted his first art exhibit, which featured his allegorical and symbolic charcoal drawings. During this exhibition, he met Mary Elizabeth Haskell, who would go on to fund Gibran's artistic development for nearly his entire life. Not only was he an artist, but he also wrote poetry and other works including The Madman, The Prophet, and Sand and Foam. He died of cirrhosis of the liver and tuberculosis on April 10, 1931.
(Bowker Author Biography)
Khalil Gibran, also known as Kahlil Gibran, was born on January 6, 1883 in Northern Lebanon. As a result of his family's poverty, he received no formal education as a small child but had regular visits from the local priest who taught him about the Bible as well as the Syrian and Arabic languages. After his father was imprisoned for embezzlement and his family's property was confiscated by the authorities, his mother decided to emigrate to the United States in 1895. They settled in Boston's South End.
He attended public school and art school, where he was introduced to the artist, photographer, and publisher Fred Holland Day. A publisher used some of Gibran's drawings for book covers in 1898. His family forced him to return to Lebanon to complete his education and learn the Arabic language. He enrolled in Madrasat-al-Hikmah, a Maronite-founded school, which offered a nationalistic curriculum partial to church writings, history and liturgy. He learned Arabic, French, and exceled in poetry. He returned to the United States in 1902.
In 1904, he hosted his first art exhibit, which featured his allegorical and symbolic charcoal drawings. During this exhibition, he met Mary Elizabeth Haskell, who would go on to fund Gibran's artistic development for nearly his entire life. Not only was he an artist, but he also wrote poetry and other works including The Madman, The Prophet, and Sand and Foam. He died of cirrhosis of the liver and tuberculosis on April 10, 1931.
(Bowker Author Biography)