Simson line theorem. The three blue points always lie on a straight line. The blue points are the closest points to the moving red point on the lines. In other words the blue points are the projections of the moving red point to the lines.
(via curiosamathematica)
Inscribed in a grid of 2n-by-2n cells is a circle with diameter 2n - 1. How many cells include a segment of the circle?
The count grows simply as 8n - 4. How would you show that?
Awesome question.
(via curiosamathematica)
Geometry Matters:
Various nature elements that abide by geometric laws and construction patterns.
© Geometrymatters,2014
(via geometrymatters)
We have three colored segment in this animation. Surprisingly the length of the longest one is always the sum of the length of the two smaller ones.
This is actually a very special case of Ptolemy’s theorem. The theorem gives a connection between the sides and the diagonals of a cyclic quadrilateral. In this case the length of the dashed lines is equal so the theorem can be simplified to the statement above.
(via visualizingmath)
Kanonkopf nach dem Hexagramm.
Beuroner Kunst, Ausdrucksform der Christlichen Mystik
Josef Kreitmeier
Freiburg im Breisgau: Herder & Co., G.m.b.H., Verlagsbuchhandlung, 1921.
