September 14, 2014
blastedheath:

Rolph Scarlett (American, 1889-1984), Untitled (Abstract Composition). Oil on canvas, 48 1/4 x 50 1/8 in.

blastedheath:

Rolph Scarlett (American, 1889-1984), Untitled (Abstract Composition). Oil on canvas, 48 1/4 x 50 1/8 in.

September 12, 2014
ryannordkitchen:

Dufy

ryannordkitchen:

Dufy

September 12, 2014

dischord:

Antelope @ Fort Reno, 2007.

September 11, 2014
matthen:

A roulette traced from rolling an ellipse inside a circle. [thanks] [code]

matthen:

A roulette traced from rolling an ellipse inside a circle. [thanks] [code]

September 11, 2014
Word of the Day

perambulator |pəˈrambyəˌlātər|

noun

a machine, similar to an odometer, for measuring distances by means of a large wheel pushed along the ground by a long handle, with a mechanism for recording the revolutions.

Brit.a baby carriage; pram.

ORIGIN early 17th cent.

September 11, 2014

rkherman:

Organisms that spend part of their life cycle as plankton are called meroplankton. These are usually the larval or early stages of reef creatures such as sea urchins, sea stars, crustaceans, worms, gastropods, and fish. Meroplankton either feed on the nutrients from the egg they hatched from, or they feed on other plankton. Meroplankton also look vastly different from their adult forms, and in the past the larvae were believed to be completely different species from the adults.

Source: http://en.wikipedia.org/wiki/Meroplankton

Species featured:

Common starfish (Asterias rubens

Green crab (Carcinus maenas)

Moon jellyfish (Aurelia aurita)

Peacock mantis shrimp (Odontodactylus scyllarus)

Common octopus (Octopus vulgaris)

Purple sea urchin (Strongylocentrotus purpuratus)

Nemertean worm (Micrura alaskensis)

—————

Inspired by Rosemary Mosco's "When I Grow Up…"

September 6, 2014
fouriestseries:

Taylor Series Approximations
A Taylor series is a way to represent a function in terms of polynomials. Since polynomials are usually much easier to work with than complicated functions, Taylor series have numerous applications in both math and physics.
There are many equations in physics — like the one describing the motion of a pendulum — that are impossible to solve in terms of elementary functions. “Approximations using the first few terms of a Taylor series can make [these] otherwise unsolvable problems” solvable for a restricted area of interest [1].
The GIF above shows the five-term Taylor series approximation of a sine wave about x=0.
Mathematica code:
f[x_] := Sin[x]
ts[x_, a_, nmax_] := 
    Sum[(Derivative[n][f][a]/n!)*(x - a)^n, {n, 0, nmax}]
Manipulate[Plot[{f[x], ts[x, 0, nmax]}, {x, -2*Pi, 2*Pi}, 
    PlotRange -> {-1.45, 1.45}, 
    PlotStyle -> {{Thick, Cyan}, {Thick, Dotted, Yellow}}, 
    AxesStyle -> LightGray, Background -> Darker[Gray, 0.8]], 
    {nmax, 1, 30, 1}]

fouriestseries:

Taylor Series Approximations

A Taylor series is a way to represent a function in terms of polynomialsSince polynomials are usually much easier to work with than complicated functions, Taylor series have numerous applications in both math and physics.

There are many equations in physics — like the one describing the motion of a pendulum — that are impossible to solve in terms of elementary functions. “Approximations using the first few terms of a Taylor series can make [these] otherwise unsolvable problems” solvable for a restricted area of interest [1].

The GIF above shows the five-term Taylor series approximation of a sine wave about x=0.

Mathematica code:

f[x_] := Sin[x]
ts[x_, a_, nmax_] := 
    Sum[(Derivative[n][f][a]/n!)*(x - a)^n, {n, 0, nmax}]
Manipulate[Plot[{f[x], ts[x, 0, nmax]}, {x, -2*Pi, 2*Pi}, 
    PlotRange -> {-1.45, 1.45}, 
    PlotStyle -> {{Thick, Cyan}, {Thick, Dotted, Yellow}}, 
    AxesStyle -> LightGray, Background -> Darker[Gray, 0.8]], 
    {nmax, 1, 30, 1}]

(via cloois)

September 4, 2014
italocontador:

-Mi calle en primavera, Putaendo (después de Raúl Pizarro).  Originalmente este es un óleo de Raúl Pizarro pintado en 1992, reversionado aquí por Italo Contador.http://badsequencer.wix.com/italocontador

italocontador:

-Mi calle en primavera, Putaendo (después de Raúl Pizarro).
Originalmente este es un óleo de Raúl Pizarro pintado en 1992, reversionado aquí por Italo Contador.
http://badsequencer.wix.com/italocontador

September 3, 2014
tornhawk:

Russo’s “Wild Metals” 12” now available from Valcrond Video:
http://www.juno.co.uk/products/russo-wild-metals/531002-01/

tornhawk:

Russo’s “Wild Metals” 12” now available from Valcrond Video:

http://www.juno.co.uk/products/russo-wild-metals/531002-01/

(via austinhays)

September 3, 2014
gills:

curtis miller

gills:

curtis miller

(via austinhays)

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