More artworks using the same procedure, but this time colours are assigned with other algorithms. Titles "Mono 1", "To heal the wound", "Not squares", and "Hot!".
#TilingTuesday #MathArt #Mathematics #quadrilateral #modernart #ArtistsOnMastodon #GenArt #algorithmicArt
I have devised a new algorithm for #tiling, this time not restricted to rectangles, but for general convex quadrilaterals. Starting from a convex quadrilateral, divide it in two, by splitting the pair of longest opposite sides into two fixed proportions (one for the larger side, one for the smaller), joining the cutting points with a segment, and iterating recursively. Some of the artworks I got, by stopping recursion depending on the position of the quadrilateral on the canvas. In these artworks, the colour of each quadrilateral is assigned depending on its shape (relative size of its sides, and sometimes of its diagonals), with absolute size affecting brightness as well. Colours in each artwork depend as well on how each computed value is assigned to RGB values, but even when it is the same, as in the first and second pictures, results are quite different when generated quadrilaterals are. Titles of these works are "Precious walk", "Jam session", "Visit to the flower garden", and "Life paths".
#TilingTuesday #MathArt #Mathematics #quadrilateral #modernart #ArtistsOnMastodon #GenArt #algorithmicArt

@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

Bilinear interpolation on a quadrilateral using Barycentric coordinates

A new algebraic method for hardware-accelerated bilinear interpolation on convex quadrilaterals is presented, using the Barycentric coordinate feature of modern GPUs.

AMD GPUOpen
Quadrilateral

Explore the properties of and relationships between named four-sided shapes by moving sides and corners of a quadrilateral.

PhET

#quadrilateral : having four sides, and consequently four angles

- Italian: quadrilatero

- Portuguese: quadrilateral

- Spanish: cuadrilátero

------------

Learn more languages @ https://wordofthehour.org/r/more

Word of The Hour

Word of the Hour helps expand your vocabulary. Every hour, a new vocabulary word is featured along with translations into 10+ languages including French, German, Hindi, Italian, Portuguese, Spanish, and more. We are supported by our warm and welcoming community on Reddit.

#quadrilateral : having four sides, and consequently four angles

- Italian: quadrilatero

- Portuguese: quadrilateral

- Spanish: cuadrilátero

------------------

Try out the Word of The Hour App @ https://wordofthehour.org

Word of The Hour

Word of the Hour helps expand your vocabulary. Every hour, a new vocabulary word is featured along with translations into 10+ languages including French, German, Hindi, Italian, Portuguese, Spanish, and more. We are supported by our warm and welcoming community on Reddit.

#quadrilateral : having four sides, and consequently four angles

- Italian: quadrilatero

- Portuguese: quadrilateral

- Spanish: cuadrilátero

------------------

Fill in missing translation @ https://redd.it/95v7rk

We need your help!! Help us improve our translations. :) : Word_of_The_Hour