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The brachistochrone
This animation is about one of the most significant problems in the history of mathematics: the brachistochrone challenge.
If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?
Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.
Johann Bernoulli posed the problem to
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7:17 PM | Terrazas

Terrazas
by Ricardo Baigorria
http://im-possible.info/english/art/montage/baigorria.html#terrazas
Author - http://rbai.deviantart.com/

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4:00 PM | Adding Economic Noise

Two months ago the New York Times had a very informative visualization of monthly economic data with added variability due to sampling error. In the above screen shot we can see how repeated sampling variability can change a steady job growth graph to many different shapes of what it might have looked like with repeated sampling.Here is another viewing an accelerating job growth graph and one possible result of the same graph with sampling variability showing very stable job growth, via
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2:57 PM | Coming Soon: More New Math TV

(Click on the comic if you can't see the full image.) (C)Copyright 2014, C. Burke.And wait until you see the New Five! He's like the old Five, but new.

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Personal data collection keeps getting easier and more efficient. Much of what was manual or clunky a few years ago …

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mathani:
Two curves cut all circles at right angles: straight line and a tractrix.
I didn’t know what a tractrix was, so I Googled it! Tractrix definition from Wikipedia: Tractrix (from the Latin verb trahere ”pull, drag”; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a tractor (pulling) point that moves at a right angle to the initial line between the object and
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6:02 PM | Escher Plumbing

Escherlike Plumbing
by Walt Foegelle
http://im-possible.info/english/art/computer/walt-foegelle.html
Author - http://fineartamerica.com/profiles/walt-foegelle.html

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[In reference to this post] At the time, I had been collecting for 2-3 years, but that was almost a year ago. My collection had definitely grown since then! Most of them can be bought @ HKNowStore.com, which sells nothing but puzzles. A few were handmade by modifying existing puzzles. Of the puzzles in those pictures, there are only two that I have not solved [the big nearly-spherical one in the middle and the one in the very bottom left corner]. I need to post a new collection photo. Sometime
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I found this type of mathematics most mind-blowing. It has greatly improved the quality of my life. I highly recommend it. Find more at: http://www.reddit.com/r/mathpics

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hyrodium:
I made the drawing figure of 1/x with desmos graphing calculator. :D
https://www.desmos.com/calculator/estpj0i9ou
http://hyrodium.tumblr.com/post/88457573594/how-to-draw-an-inverse-of-a-1-draw-a-unit

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10:05 PM | Math/Educator Website Links

The following are a bunch of links from pages I ripped out of teacher magazines. I haven't visited any of them despite having these pages for a very long time. So I'm sharing them here so I can look at them sometime in the future and clean up some of the random clutter on my desk at home. CC.BetterLesson.com/mtp: More than 3000 classroom-ready lessons that can be integrated into any curriculum. Lessons created by more than 130 Master Teachers, with step-by-step instructions, videos, thoughts
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curiosamathematica:
A curved variant of the Sierpiński fractal.

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6:34 PM | New images by Regolino Bizzi

14 new artworks by Regolino Bizzi
http://im-possible.info/english/art/various/odonodo.html#a47

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s-c-i-guy:
Cells lining the blood vessel walls
The structure of the endothelium, the thin layer of cells that line our arteries and veins, is visible here. The endothelium is like a gatekeeper, controlling the movement of materials into and out of the bloodstream. Endothelial cells are held tightly together by specialized proteins that function like strong ropes (red) and others that act like cement (blue).
Image courtesy of Christopher V. Carman and Roberta Martinelli, Harvard Medical
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spaceplasma:
Microwave Induced Plasma
This coaxial microwave plasma source (MPS) generates plasma without using a magnetic field. It works like an inverse luminescent tube excited by microwaves. The coaxial microwave plasma generator consists of a copper rod (antenna) as inner conductor surrounded by quartz tube filled with argon gas, the plasma is the outer conductor. The inside of the tube is at atmospheric pressure whereas the outside is at low pressure. The plasma formed around the quartz
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3:04 PM | Flights around Ukraine

The New York Times is covering Malaysia Airlines Flight 17 with a series of maps. The ones above show a …

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8:23 AM | Geologic map of Mars

The USGS released a more detailed geologic map of Mars, not just renderings based on rough models. The USGS-led mapping …

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Submitted by Manuvstheworld:
Fanfiction, Graphs, and PageRank
On a website called fanfiction.net, users write millions of stories about their favorite stories. They have diverse opinions about them. They love some stories, and hate others. The opinions are noisy, and it’s hard to see the big picture.
With tools from mathematics and some helpful software, however, we can visualize the underlying structure.
In the following post, we will visualize the Harry Potter, Naruto and Twilight fandoms
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7:28 PM | Tattoo with impossible triangle

Tattoo by Chaim Machlev
http://im-possible.info/english/art/misc/tattoo/chaim-machlev.html
Author - https://www.facebook.com/chaim.machlev

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Chinese Artist Exhibits Gorgeous ‘Sculptures’ Built By Bees
The Huffington Post | By Mallika Rao
The Beijing-based artist and beekeeper Ren Ri is a focused man. His new three-part series — titled “Yuansu” in reference to the Chinese word for “element” — turns bees into his collaborators. Yuansu II features sculptures made by bees, of beeswax.
In an interview with CoolHunting, Ren explains the “special” properties that make beeswax such an interesting
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5:23 PM | Useless Junk

(Click on the cartoon to see the full image.) (C)Copyright 2014, C. Burke.I just have to make sure that I don't make it on her list.

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LeBron James decided to head back to Cleveland, so naturally the odds that they win the championship went up. Todd …

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ipiphi:
Let \(S_n (z) = \sum_{k=0}^n z^k \) then parametrize \(S_n\) on circles in the complex plane centered at the origin. The animation shows the graph of the real part of \(S_{100} (r e^{2\pi i t})\) as a function of \(t\) and how it changes as \(r\) ranges from \(0\) to \(1\).

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3mbicommission:
After looking into platonic solids earlier in my project, I began to look at other forms of polyhedra in order to form 3D structures relevant to my ideas. This above image displays Wenzel Jamnitzer’s few of many explorations of solid forms known as polyhedra, which are based on the five platonic solids. Polyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia. Seeing as I have been working with very simple
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7:07 PM | Inside the Death Star

Inside the Death Star
by Super7
http://im-possible.info/russian/art/escher-inspired/super7.html
Author - http://super7store.com/

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crookedindifference:
Read the Apollo 11 Flight Plan in Its 353-Page Entirety
Exactly 45 years ago today, after months of preparation, Apollo 11 embarked on its now-legendary mission to the moon. But what exactly does it take to send three men into the great, vacuous unknown? See for yourself.
This 353-page document is the entire Apollo 11 flight plan in all its scientific glory. And if it gets a little confusing it’s because this is one of those rare cases where, yes, it
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underthesymmetree:
Phi - The Golden Ratio presents itself everywhere in life, from basic geometry & crystal formations, to plants, planetary ratios and galactic formations. It is the most efficient ratio under near-perfect systems.
Read the Book | Follow

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9:21 AM | How much underwear to bring on a trip

Packing underwear for a short trip is easy. You just pack a pair for each day you're away. However, longer …

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11:35 PM | Great Mistakes

I caught a cute feature about Einstein on NPR. It is a quick 4 minute listen. It should make you feel better the next time you make a sign mistake to know that you are in great company.

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\[(n+1)^3 - n^3 \equiv 1 \mod 6\] Claudi Alsina,, Roger Nelsen,, & Hasan Unal (2014). Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6 The College Mathematics Journal, 45 (2), 135-135 DOI: 10.4169/college.math.j.45.2.135 (facebook)

Claudi Alsina,, Roger Nelsen, & Hasan Unal (2014). Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6, The College Mathematics Journal, 45 (2) 135-135. DOI: 10.4169/college.math.j.45.2.135

Citation

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\[(n+1)^3 - n^3 \equiv 1 \mod 6\] Claudi Alsina,, Roger Nelsen,, & Hasan Unal (2014). Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6 The College Mathematics Journal, 45 (2), 135-135 DOI: 10.4169/college.math.j.45.2.135 (facebook)...
Claudi Alsina,, Roger Nelsen,, & Hasan Unal. (2014) Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6. The College Mathematics Journal, 45(2), 135-135.
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Claudi Alsina,, Roger Nelsen, & Hasan Unal (2014). Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6, The College Mathematics Journal, 45 (2) 135-135. DOI: 10.4169/college.math.j.45.2.135

Citation

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La settimana scorsa, su twitter, ho diffuso alcune immagini, foto scattate dalle pagine dal volume Letture da Le Scienze: Fisica delle particelle (un indice del volume), che raccoglieva alcuni articoli usciti sulla rivista italiana (e quindi anche su Scientific American). Poiché ognuna di quelle immagini fa inevitabilmente parte della storia della fisica, mi sembra sensato proporle raccolte insieme in un unico post molto più semplicemente raggiungibile di tanti piccoli... cinguettii.
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Weisskopf, V. (1968). The Three Spectroscopies, Scientific American, 218 (5) 15-29. DOI: 10.1038/scientificamerican0568-15

Barish, B. (1973). Experiments with Neutrino Beams, Scientific American, 229 (2) 30-38. DOI: 10.1038/scientificamerican0873-30

Treiman, S. (1959). The Weak Interactions, Scientific American, 200 (3) 72-84. DOI: 10.1038/scientificamerican0359-72

Cline D.B., Mann A.K. & Rubbia C. (1974). The Detection of Neutral Weak Currents, Scientific American, 231 (6) 108-119. DOI: 10.1038/scientificamerican1274-108

Glashow, S. (1975). Quarks with Color and Flavor, Scientific American, 233 (4) 38-50. DOI: 10.1038/scientificamerican1075-38

Nambu, Y. (1976). The Confinement of Quarks, Scientific American, 235 (5) 48-61. DOI: 10.1038/scientificamerican1176-48

Johnson, K. (1979). The Bag Model of Quark Confinement, Scientific American, 241 (1) 112-121. DOI: 10.1038/scientificamerican0779-112

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#sand #battery #chemistry #energy This is the holy grail – a low cost, non-toxic, environmentally friendly way to produce high performance lithium ion battery anodesZachary FavorsSchematic of the heat scavenger-assisted Mg reduction process.Herein, porous nano-silicon has been synthesized via a highly scalable heat scavenger-assisted magnesiothermic reduction of beach sand. This environmentally benign, highly abundant, and low cost SiO2 source allows for production of nano-silicon at the
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Favors, Z., Wang, W., Bay, H., Mutlu, Z., Ahmed, K., Liu, C., Ozkan, M. & Ozkan, C. (2014). Scalable Synthesis of Nano-Silicon from Beach Sand for Long Cycle Life Li-ion Batteries, Scientific Reports, 4 DOI: 10.1038/srep05623

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Nel momento in cui affermiamo che un dato numero è primo, ovvero nel momento in cui affermiamo matematicamente che $n$ è un numero primostiamo, in effetti, affermando che $n$ è un numero naturale divisibile solo per se stesso e per l'unità. Questa definizione può però essere ulteriormente ridotta come segue(1): $n$ è un numero naturale e, presi comunque due numeri naturali $h$ e $k$, se $n$ è $h \cdot k$, allora $h$ o $k$ è 1.E' chiaro, in questo caso, che il senso di riduzione per una […]

Quine, W. V. (1964). The Foundations of Mathematics, Scientific American, 211 (3) 112-127. DOI: 10.1038/scientificamerican0964-112

Paul J. Cohen & Reuben Hersh (1967). Non-Cantorian Set Theory, Scientific American, 217 (6) 104-116. DOI: 10.1038/scientificamerican1267-104

Howard DeLong (1971). Unsolved Problems in Arithmetic, Scientific American, 224 (3) 50-60. DOI: 10.1038/scientificamerican0371-50

Kurt Gödel (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, 38-38 (1) 173-198. DOI: 10.1007/BF01700692

Zermelo, E. (1904). Beweis, dass jede Menge wohlgeordnet werden kann, Mathematische Annalen, 59 (4) 514-516. DOI: 10.1007/BF01445300

Kurt Gödel (1938). The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis, Proceedings of the National Academy of Sciences, 24 (12) 556-557. DOI: 10.1073/pnas.24.12.556

Paul J. Cohen (1963). The independence of the continuum hypothesis, Proceedings of the National Academy of Sciences, 50 (6) 1143-1148. DOI: 10.1073/pnas.50.6.1143

Paul J. Cohen (1964). The independence of the continuum hypothesis, II, Proceedings of the National Academy of Sciences, 51 (1) 105-110. DOI: 10.1073/pnas.51.1.105

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jesusem tweeted: @jesusem

RT @la_tuerka: La Tuerka ha enviado una invitación formal a @EsperanzAguirre para que acuda al programa en septiembre. Respuesta afirmativa…

2014-07-22 12:37:19

MindAfterMath tweeted: @MindAfterMath

2014-07-22 12:36:55

michiexile tweeted: @michiexile

RT @Eorlingur: @michiexile 22/7 is the rational choice for pi approximation day #therealpiday #badabing

2014-07-22 12:32:39

ulaulaman tweeted: @ulaulaman

DropSea: I sotterranei http://t.co/oFo6WNGUHY by @elyfil

2014-07-22 12:27:10

j_lanier tweeted: @j_lanier

What's round on the ends and #tmc14 in the middle? http://t.co/ZF2LNNaEKt

2014-07-22 12:23:11

j_lanier tweeted: @j_lanier

Exit 0. West Virginia takes a stand on the natural numbers controversy. #tmc14 http://t.co/huJjXbzuHd

2014-07-22 12:19:36

j_lanier tweeted: @j_lanier

.@mpershan A pair of 6-gons! They're Utahs! http://t.co/jdFeXuOvdX

2014-07-22 12:12:32

CardColm tweeted: @CardColm

RT @WWMGT: Three squares (Lyber Katz) http://t.co/tRQRTyrgXK squares.pdf (warning, solutions included. Try to solve it as soon as you read …

2014-07-22 12:11:53

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