Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T08:16:41.789Z Has data issue: false hasContentIssue false

The Division of the Circle—Concluded

Published online by Cambridge University Press:  03 November 2016

Extract

To establish the order of the locus we must note that besides the above mentioned n intersections with the circumference, the point D also belongs to the curve, so that the latter cuts the circle in n+1 points. The order of the curve is therefore Let n be even.

The ratio is not an integer, so that a complete rotation of the straight line BC must take place before the two generating straight lines can be in their initial mutual position; the line revolving round D will be, after a semi-rotation of BC, parallel to BC in DE, and we may say that all the loci for n = 2p are asymptotic in the direction BC, on account of the initial position of BC and DA.

Type
Research Article
Copyright
Copyright © The Mathematical Association 1909

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)