themaninthegreenshirt:

Friedrich Nietzsche’s typewriter, the Hansen Writing Ball

During his final decade, Friedrich Nietzsche’s worsening constitution continued to plague the philosopher. In addition to having suffered from incapacitating indigestion, insomnia, and migraines for much of his life, the 1880’s brought about a dramatic deterioration in Nietzsche’s eyesight, with a doctor noting that his “right eye could only perceive mistaken and distorted images.” Nietzsche himself declared that writing and reading for more than twenty minutes had grown excessively painful. With his intellectual output reaching its peak during this period, Nietzsche required a device that would let him write while making minimal demands on his vision. So he sought to buy a typewriter in 1881. Although he was aware of Remington typewriters, the ailing philosopher looked for a model that would be fairly portable, allowing him to travel, when necessary, to more salubrious climates. The Malling-Hansen Writing Ball seemed to fit the bill.

Cite Arrow via sometheoryofsampling
Comments (View)

spring-of-mathematics:

Crystal Animation Frames: From “Before iterating” to Iteration 9. - Image by Eric Green.

Frost crystals and snowflakes form are so abundant. Some frost crystals formed naturally and also illustrate fractal process development. (Illustrations image by Alexey Kljatov - source). 

Cite Arrow via mjvazcosta
Comments (View)
thechivalrousfox:

A transparent ghostie friend for all of your spoopy needs

thechivalrousfox:

A transparent ghostie friend for all of your spoopy needs

Cite Arrow via scientistsarepeopletoo
Comments (View)

mathhombre:

Kandinsky generator.

Poking around GGBtube I found Jean-Paul Berroir’s cool Mondrian generator. Very slick. (I was thinking about that recently, too.) I was excited to click on his Kandinsky generator. Fun GeoGebra, but didn’t look much like Wassily’s work to me.

So I had to make my own. (On GeoGebraTube.)

This sketch makes random points, draws Bezier curves through sets of four of those, then flips a coin to decide whether they are shown. Also a few geometric points.

Is it art?

Wassily Kandinsky, 1866-1944, was the world’s first modern abstract artist. Find out more about his amazing work, http://www.wassilykandinsky.net/.

If you download the sketch, there is a tool to find the point that determines a degree 4 Bezier curve. To make the curve, type Locus[<ptname>,t]. t is a slider off screen (has to be showing to make a locus) that runs from 0 to 1.

Every few clicks, the painting will animate. Kandinsky would totally be into animation, I think.

What would you add?

Cite Arrow via mathhombre
Comments (View)
placidiappunti:

(via @SaraBentivegna )

xké me lo kiedi?

placidiappunti:

(via @SaraBentivegna )

xké me lo kiedi?

Cite Arrow via placidiappunti
Comments (View)

fouriestseries:

Curves of Constant Width and Odd-Sided Reuleaux Polygons

A curve of constant width is a convex, two-dimensional shape that, when rotated inside a square, always makes contact with all four sides.

A circle is the most obvious (but somewhat trivial) example. Some non-trivial examples are the odd-sided Reuleaux polygons — the first four of which are shown above.

Since they don’t have fixed axes of rotation, curves of constant width (except the circle) have few practical applications. One notable use of the Reuleaux triangle, though, is in drilling holes in the shape of a slightly rounded square (watch one of the triangle’s vertices and notice the shape it traces out as it spins).

On a less technical note, all curves of constant width are solutions to the brainteaser, “Other than a circle, what shape can you make a manhole cover such that it can’t fall through the hole it covers?”

Mathematica code posted here.

Additional source not linked above.

Cite Arrow via quantumvyp3r
Comments (View)

intothecontinuum:

(click through the images to view in high-res)

Penrose tilings are an example of the non-periodic tilings discussed in the last post. Recall that these are tilings that cover the entire infinite plane leaving neither gaps nor overlaps. Whats nice about these tilings is that the set of tiles used to construct the Penrose tilings only consists of two different basic shapes consisting of quadrilaterals

Whats even more remarkable about Penrose tilings is that using just these two shapes it is possible to construct infinitely many different tilings that cover the infinite plane. This infinity is infinitely bigger in size than the countable infinity of the whole numbers ( 1, 2, 3, 4, and so on), but rather equivalent to the uncountable infinity associated to the real numbers (which includes all whole numbers, fractions, and decimals with infinitely many digits).

Despite the existence of these infinitely many different Penrose tilings, there is one peculiar property they all exhibit. Consider any finite region, or patch, of one particular Penrose tiling. Then it is possible to find an exact copy of this patch in any other different Penrose tiling! Moreover, this patch occurs infinitely often in different spots in any given tiling! Note that this is true of any patch of any size no matter how big as long as its finite. This implies that if you were only able to examine a finite part of any Penrose tiling, you could never really distinguish that entire tiling from any other tiling. Thus, different Penrose tilings are only perfectly distinguishable in the infinite limit of the entire plane.

The images shown above display finite regions of Penrose tilings. They are constructed using an elegant "cut-and-project" method (also used here), which involves projecting the points of the integer lattice in 5-dimensional Euclidean space, onto a certain 2-dimensional plane. Connecting adjacent projected points in this plane by lines then yields a Penrose tiling.

Further reading:

Image Source: Wikipedia

Cite Arrow via scientistsarepeopletoo
Comments (View)

(Source: museumuesum)

Cite Arrow via imamathlover
Comments (View)
wackystuff:

Where God Lives in the Human Brain (by wackystuff)

wackystuff:

Where God Lives in the Human Brain (by wackystuff)

Cite Arrow via wackystuff
Comments (View)
Cite Arrow via an7i
Comments (View)

hyrodium:

The gif animation of folding the net of the tesseract(8-cell). ;-)

There are many kinds of the net of the tesseract.

http://hyrodium.tumblr.com/post/67134693288/hyrodiums-photostream-on-flickr-there-are-many

Cite Arrow via mjvazcosta
Comments (View)
fyeahastropics:

A Milky Way Band Credit &amp; Copyright: John P. Gleason, Celestial Images
Explanation: Most bright stars in our Milky Way Galaxy reside in a disk. Since our Sun also resides in this disk, these stars appear to us as a diffuse band that circles the sky. The above panoramaof a northern band of the Milky Way’s disk covers 90 degrees and is a digitally created mosaic of several independent exposures. Scrolling right will display the rest of this spectacular picture. Visible are many bright stars, dark dust lanes, red emission nebulae, blue reflection nebulae, and clusters of stars. In addition to all this matter that we can see, astronomers suspect there exists even more dark matter that we cannot see.

fyeahastropics:

A Milky Way Band 
Credit & CopyrightJohn P. Gleason, Celestial Images

Explanation: Most bright stars in our Milky Way Galaxy reside in a disk. Since our Sun also resides in this disk, these stars appear to us as a diffuse band that circles the sky. The above panoramaof a northern band of the Milky Way’s disk covers 90 degrees and is a digitally created mosaic of several independent exposures. Scrolling right will display the rest of this spectacular picture. Visible are many bright starsdark dust lanesred emission nebulaeblue reflection nebulae, and clusters of stars. In addition to all this matter that we can see, astronomers suspect there exists even more dark matter that we cannot see.

Cite Arrow via fyeahastropics
Comments (View)

mathhombre:

Polygon Pattern.

Any questions?

(Note: finally carried out a successful Execute command for this, to make separately coloring rows a little easier. EDIT: added a zoomed out gif.)

Among all the counting questions, I like this one for the “does the first step fit the pattern?”

Cite Arrow via mathhombre
Comments (View)