• Journal for History of Mathematics
• /
• v.17 no.4
• /
• pp.101-122
• /
• 2004

It has been always the issue to discuss 'how we teach mathematics' for the mathematical learning. As for an answer to this, it was suggested to use the history of mathematics. The reason is simple that is, the education of mathematics requires to understand mathematics and to know the history of mathematics is effective for mathematical understanding. In particular, the history of algebra was discussed to some extent as an illustration. This study focuses on the history of geometry from this point of view. We review the history of geometry by comparison in terms of three criteria from the origin of geometry to modem differential geometry in the middle of the 20th century, which are backgrounds (inner or outer ones), characterizations (approach, method, object), influences to modem mathematics. As an application of such historical data to the education of mathematics, we pose the problem to determine the order of instruction in mathematics.