Centroid of a parabolic Segment by construction

jonbenedick shared this question 5 years ago

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Is there a way to locate the centroid of a parabolic segment by construction only? (without using integration and formula)

Comments (5)

Simona Riva ● 5 years ago

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.

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jonbenedick ● 5 years ago

Thanks mathmum, I already viewed the document, but still I have no idea on locating the centroid inspite of the information.

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Roman Chijner ● 5 years ago

Hi all

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

Roman Chijner

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Roman Chijner ● 5 years ago

Hi, Noel

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.

are examples

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slicing ● 5 years ago

Nice solution! Geogebra allows to locate K point by means of vector command. Cheers af39799a9b3655cb14449c1de0def1bc

Files: pcentroid.png

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