@ColinTheMathmo @GerardWestendorp
OK, here’s a counterexample with mostly nice numbers.
It wasn’t easy to find because when all numbers are ‘nice’ then the proposed theorem usually holds true 😆 e.g. rhombus, parallelogram, etc.
#geometry #iTeachMath #puzzle #quadrilateral #midpoint #geogebra
#geometry #iTeachMath #puzzle #quadrilateral #midpoint #geogebra
@ColinTheMathmo @GerardWestendorp I thought a simpler problem might help, i.e. https://en.wikipedia.org/wiki/Varignon%27s_theorem
However, I then found some counter-examples showing a small divergence from the desired area. I need to be sure that these aren't rounding errors
#geometry #iTeachMath #puzzle #quadrilateral #midpoint #geogebra
@ColinTheMathmo Nice, I expected shearing to preserve the fraction, e.g. rhombus, but not work for the second quadrilateral. Works nicely #geogebra and other dynamic geometry software.
The closest to a counter-example I found were concave quadrilaterals and quadrilaterals with three points colinear (a triangle so a bit of a cheat)
2 animations #geogebra pour illustrer la lecture de l'heure solaire de nuit avec un nocturlabe.
1e animation : déplacement de la constellation de la Grande Ourse au fil du temps.
www.geogebra.org/m/rnpsz2rg
1/2
El Pulpito et l'homothécie.
#geogebra . https://www.geogebra.org/m/jba76dcw
#pulpo #dilatation #homothécie #geometry #fun #iTeachMaths #geogebra
El Pulpito et la translation.
foldworks
Jean-Baptiste Etienne
David ALBERTO