53. Ptolemy's Theorem by Area Formulae

1960 ◽  
Vol 44 (348) ◽  
pp. 112
Author(s):  
James J. Callagy
Keyword(s):  
Ptolemy’S Theorem

Ptolemy's Theorem and Regular Polygons

1946 ◽  
Vol 39 (3) ◽  
pp. 117-120
Author(s):  
L. S. Shively
Keyword(s):  
Point Of View ◽  
Elementary Geometry ◽  
Relative Importance ◽  
Regular Polygons ◽  
Ptolemy’S Theorem ◽  
High Place ◽  
Geometric Study

It might be both profitable and interesting to attempt to evaluate the relative importance of some of the outstanding theorems of elementary geometry by means of a poll of mathematicians. If this were done, there is little doubt that the theorem of Pythagoras would in the opinion of most people, head the list. It is not so clear just how other important theorems would be ranked. But without doubt, Ptolemy's theorem concerning an inscribed quadrilateral is deserving of a high place. This judgemnt is warranted, both from the point of view of the use which Ptolemy made of it, and from a consideration of its power as a tool for geometric study.

Proof Without Words: Ptolemy's Theorem

2012 ◽  
Vol 43 (5) ◽  
pp. 386-386
Author(s):  
William Derrick ◽  
James Hirstein
Keyword(s):  
Ptolemy’S Theorem

The number of intersections of random chords to a circle — third and fourth moments

1982 ◽  
Vol 19 (2) ◽  
pp. 355-372 ◽  
Author(s):  
John Gates
Keyword(s):  
Reduction Technique ◽  
Ptolemy’S Theorem ◽  
Skewness And Kurtosis

In this paper the distributions of the number of intersections of three, four and five random chords to a circle are obtained by a reduction technique employing Ptolemy's theorem. These results are then used to obtain the skewness and kurtosis of the number of intersections of n random chords to a circle.

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