In his book "Die Sonnenuhr und ihre Theorie" (The sundial and his theory) Jörg Meyer writes on page 200 (my English translation): Through the point P where all the hour lines of any sundial come together, a circle is drawn. The center M and the radius of the circle are irrelevant. The hour lines whose hour angle differ from each 6 hours or 90 ° were grouped into pairs. The points where the hour lines of a pair intersect the circle, are connected with a chord (a straight line joining the ends of an arc ) Then is applicable: all these chords pass through a common point Q.  In the study of this case and assuming that the projection of a circle is an ellipse and vice versa, I found out (graphic) the theorem: Of all right triangles, inscribed in an ellipse, of which the right angle point (point P) is common, the hypotenuses intersect in the same point (point S). See drawing. Who can prove this theorem? Willy Leenders Hasselt in Flanders (Belgium) Visit my website about the sundials in the province of Limburg (Flanders) with a section 'worth knowing about sundials' (mostly in Dutch): http://www.wijzerweb.be |
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