randform

One of the first mathematical visualization clips if not the first is: the impossible map by Evelyn Lambart from 1947. In the film it is explained how to find coordinate maps for a sphere, partially exemplified with a grapefruit.

Evelyn Lambart is usually in the shadow of her frequent collaborator Norman McLaren, with whom she worked together in the fifties.

They both liked to play with graphical and likewise mathematical “entities”, like lines and shapes in the interplay with coulours:
Caprice en Couleurs (1949)
Around is Around (1951)
Horizontal Lines (1962)
Vertical Lines (1960)

But both have in their animations also more “lifelike” shapes, like birds and variation of birds, which are coloured but which are mostly “flat” reminding of “shadow figures” like e.g. in the animations of Charlotte Reiniger. This was partially due to their cut-out and scratching techniques. However also real life appears in their films. Evelyn Lambart did a lot of illustrative animations for other science films, but also for e.g. the film: A Chairy Tale, which reminds me of the earlier mentioned Georges Méliès. (Watch e.g. his film “Un homme de tete” from 1898, which is currently on youtube.com)

Remark: It seems that since two days there is Blinkity Blank by Norman McLaren on Youtube.com, and also parts of Prince Achmed by Lotte Reiniger. I dont know how long the films will be there, and what copyright problems are involved with them, thats why I dont link them.

update 11.10.10: An approximate and by no means accurate visual demonstration of the proposition that the area of a sphere is four times the area of its circular shadow (look also at this comment)

Take half an orange:

Peel the half orange in a spiral. You peel the spiral in such a way that you go around twice in order to peel it fully, while keeping the width of the spiral arm (approx.) constant (that is you peel an archimedian or arithmetic speiral). By looking at the peeled orange one (more or less badly) sees that going around only once, one peeled off a part which covers roughly the area of the circular shadow:

Fold the spiral in the middle and put the two spiral halfs on top of each other:

One (again more or less badly) sees that the middle of the spiral is (approximately) at the point where the spiral had gone around once:

So roughly one half of the spiral covers the area of half of half of an orange (because the two folded halfs of the spiral cover half an orange). In the meantime such a half also covered the circular shadow (i.e. that what you see by looking onto the orange from above), i.e. the second half was more or less perpendicular to the viewer and was thus (almost) not visible.
This is of course no prove of the proposition but gives only a rough feeling, that the proposition could be true.

There are those parties, where you are asked in the very first minutes of a small talk, what you do in your life. And if your answer is “I am a mathematician” then the reaction is usually rather passionate. Either you found some kind of soul mate, someone who understands or – and that happens very often – you are confronted with sentences like: “Ohh – really — I always hated math – I always had problems with the math!”. Now replace “math” with “law” in the last two sentences and look what you get….—OK -put that ittle joke aside- instead of lawyer, plug in: social worker, english teacher, baseball trainer etc. You will rather rarely hear: I was always hated social sciences, english, sport etc. , whereas for math (and physics) it is the generic situation. This is because in nowadays (western?) society it is too often a good thing to dislike math.
If you are on a party it is easy to deal with that disdain – either you stick to the math lovers or you take your revenge by “Oh you just had bad teachers – let me explain the addition theorem of trigonometric functions!” :O (yes this is a nerd joke — happened out of desperation :))

However if the open dislike of math is expressed by a public person like a politician or a journalist than this isn’t fun anymore, because it involves the development of a public opinion about an issue.
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A little follow up to our earlier posts about symmetries, which were a collaborative effort with graphics designer Etienne Mineur, who contemplated at the same time about ambigrammes in a socalled mineur-randfrom Blog pong match.

Sascha Lobo from riesenmaschine found via designboom the page of ambigramme designer John Langdon and found there probably (wo hat er das denn schon wieder ausgebuddelt!) also the link of this very cool ambigramm generator.

A very worthwhile-to-visit website is the one of the US National Aeronautics and Space Administration NASA. Here one can e.g. surf to the remarkable ANTS – Autonomous NanoTechnology Swarm webpage (also autonomous in terms of graphic design…). (more…)

The above square shows the location of the only earthquake that happened near Berlin, Germany in the last seven days (more…)

A classic topic in intersections between math and art/design are tesselations. This is mostly due to the fact that the included math is almost completely visualizable, which can’t be said for most parts of mathematics.
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This is a classic. hoogerbrugge.com has been around for quite a while now. Still his catalog of flash nails, interactive videos, and stories is constantly growing (and his site got recently redesigned).
Definitely worth a visit is flow (an interactive music video) and the modern living/neurotica series. I must admit that I was kind of an addict in the years this series was a regular (1998-2001) — one of my favorites is “51 Nervous”.

Due to a high failure rate on our math test :( in the comments section we temporarily switched off the math test script (which was not written by ourselves). No – seriously we would like to excuse ourselves for any comments which got lost. Unfortunately we only just noticed that there were quite a bit of comments lost, however we couldnt recover them. Due to this we will temporarily put comments on moderation. means: your comment doesn’t appear immediately…but will appear after being checked for spam.

thanks for your patience.

“empathic paintings” by Shugrina, Betke and Collomosse

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I couldn’t resist in reblogging this. Not really out of schadenfreude but more because I like it if techology gets so human :-)

via spreeblick
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