Is there a way to locate the centroid of a parabolic segment by construction only? (without using integration and formula)
As far as I remember (I studied history of mathematics long ago!) there is a geometric result due to Archimedes.
I found this document in English that could probably help you.
Thanks mathmum, I already viewed the document, but still I have no idea on locating the centroid inspite of the information.
Very interesting problem, solved by Archimedes 2300 years ago!!! .
@ Noel Lambert :
In your applet A-point is not free . It must be between points B and C:
-Archimedes and the area of a parabolic segment by Murray Bourne, 14 Dec 2008
Archimedes Algorithm is the method of geometrical construction: without using integration and formula
Lemma 1 (Archimede’s Theorem) (http://abocci.web.cern.ch/a...)
is for A, chosen on the arc but in a special way.
Nice solution! Geogebra allows to locate K point by means of vector command. Cheers
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