Difference between revisions of "Bodenmiller theorem"
From Encyclopedia of Mathematics
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| − | Consider a complete [[Quadrilateral|quadrilateral]] with four sides | + | {{TEX|done}} |
| + | Consider a complete [[Quadrilateral|quadrilateral]] with four sides $a$, $b$, $c$, $d$ intersecting in the six points $P$, $Q$, $R$, $S$, $T$, $U$. Then the three circles that have the three diagonals $PS$, $QT$ and $RU$ as diagonals intersect in the same two points. | ||
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| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> R. Fritsch, "Remarks on Bodenmiller's theorem" ''J. of Geometry'' , '''47''' (1993) pp. 23–31</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> G. Weiss, "Eine räumliche Deutung der Vierseiteigenschaft von Bodenmiller" ''Elemente der Math.'' , '''37''' (1982) pp. 21–23</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> R. Fritsch, "Remarks on Bodenmiller's theorem" ''J. of Geometry'' , '''47''' (1993) pp. 23–31</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> G. Weiss, "Eine räumliche Deutung der Vierseiteigenschaft von Bodenmiller" ''Elemente der Math.'' , '''37''' (1982) pp. 21–23</TD></TR> | ||
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Latest revision as of 08:29, 26 March 2023
Consider a complete quadrilateral with four sides $a$, $b$, $c$, $d$ intersecting in the six points $P$, $Q$, $R$, $S$, $T$, $U$. Then the three circles that have the three diagonals $PS$, $QT$ and $RU$ as diagonals intersect in the same two points.
Figure: b110680a
References
| [a1] | R. Fritsch, "Remarks on Bodenmiller's theorem" J. of Geometry , 47 (1993) pp. 23–31 |
| [a2] | G. Weiss, "Eine räumliche Deutung der Vierseiteigenschaft von Bodenmiller" Elemente der Math. , 37 (1982) pp. 21–23 |
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How to Cite This Entry:
Bodenmiller theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bodenmiller_theorem&oldid=13366
Bodenmiller theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bodenmiller_theorem&oldid=13366
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article