• Journal for History of Mathematics
• /
• v.17 no.4
• /
• pp.77-86
• /
• 2004

Felix Klein profoundly influenced mathematical developments throughout the world by showing a new direction for modem geometry. He also influenced the lives of excellent scientists like Einstein by reforming mathematical education. The first Felix Klein medal of the Internal Commission on Mathematical Instruction was awarded at ICME-10 in July of 2004. In this article, we discuss Klein's Erlangen Program and investigate his influence on modem mathematics and mathematical education with this medal as momentum.

• Journal for History of Mathematics
• /
• v.15 no.2
• /
• pp.15-32
• /
• 2002

The first part of this thesis gives some brief explanation of the theory and history of imaginary elements in analytic geometry in the 19th century. The second part of this thesis discusses the theory of imaginary elements of synthetic geometry in the first half of the 19th century. Then the next part mentions the theory of imaginary elements of geometry in the second half of that same century. Particularly Christian von Staudt's and Felix Klein's theories are handled in this part. Von Staudt, who has completed the system of the synthetic projective geometry, used ‘involution’ in order to introduce a new concept ‘imaginary elements’- imaginary points, imaginary lines and imaginary plane-in synthetic geometry. Klein applied von Staudt's theory as he convey the result of the research in algebraic geometry in a picture. Von Staudt's and Klein's research may be regarded as the top of the effort to investigate possible relationship between real and imaginary structures.