#projective geometry

[lindahall]

Pablo Picasso – Scientist of the Day

Pablo Picasso, a Spanish painter, died Apr. 8, 1973, at the age of 91.

Learn more

[somewhat-happy-poet]

Saw a post on relationship metaphors based on mathematical concepts, and they were all very interesting and fun metaphors. The one about parallel lines, like two people who never "meet" (literally or figuratively), made me think of something, though.

I feel like someone more poetic than I am can make use of this:

Parallel lines can meet if we work in spaces other than what we're used to (what we're used to is called "Euclidean space," for those who haven't ever heard that term).

For example, if our space is a sphere, there are no such things as parallel lines.

For another example, in the growing field of projective geometry (Used in art! Math isn't only for science) we have what is called "projective space," often also called "extended Euclidean space," that includes points and lines at infinity. Thus, in projective space, parallel lines meet at infinity.

I dunno, I feel like someone could find something interesting in this. I'm a little too lethargic to do anything with this myself at the moment.

[pancaketitan]

The Lord’s Unicursal Prayer

His Madness Prevailed Over All Other Considerations

designed & vectored by me with Adobe Illustrator

Instagram

[isomorphismes]

_What is a Lefschetz pencil?_ by Robert Gompf

[lindahall]

Esprit Jouffret – Scientist of the Day

Esprit Jouffret, a French mathematician, was born Mar. 15, 1837.  

read more...

[isomorphismes]

Max Dehn, Über den Rauminhalt

Karlsruhe, 1901

allgemeine = general

ganzzahlige = integral (adjective of integer); ganz = whole

zerlegungsgleich = equidecomposable

entsprechender = appropriate

Bezeichungsweise = notation

nun = now then…

[adjoint-law]

Fundamental Theorem of Projective Geometry (abridged): following sunbeams from window to wall (or tilting a floor plan 90° to read it, or any linear mapping between planes in ℝ³ lifted via perspective to an automorphism of the points+lines of ℝ²) is, like, surprisingly easy to draw in perspective, with nothing but a straightedge.

Proposition: ...and is uniquely determined by its action on four non-collinear points

Proposition: ...and its action on a line is uniquely determined by three points.

Corollary: If there's a line going to a known vanishing point and you know the actual distance between two other points on that line, it's surprisingly easy to take measurements anywhere else on that line. With nothing but a straightedge.

[ibmathsresources]

The Tusi couple - A circle rolling inside a circle

The Tusi couple – A circle rolling inside a circle

https://giphy.com/gifs/KAe4nRWH6PlwGqnJJZ

The Tusi couple – A circle rolling inside a circle

Numberphile have done a nice video where they discuss some beautiful examplesof trigonometry and circular motion and where they present the result shown above: a circle rolling within a circle, with the individual points on the small circle showing linear motion along the diameters of the large circle.…

View On WordPress