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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}]
thescienceofreality:

project-argus:

Carl Sagan on astrology in newspapers.  From his interview with Ted Turner.
Also, photosets are fun.

I will never stop reblogging this set.
thescienceofreality:

project-argus:

Carl Sagan on astrology in newspapers.  From his interview with Ted Turner.
Also, photosets are fun.

I will never stop reblogging this set.
thescienceofreality:

project-argus:

Carl Sagan on astrology in newspapers.  From his interview with Ted Turner.
Also, photosets are fun.

I will never stop reblogging this set.
thescienceofreality:

project-argus:

Carl Sagan on astrology in newspapers.  From his interview with Ted Turner.
Also, photosets are fun.

I will never stop reblogging this set.

thescienceofreality:

project-argus:

Carl Sagan on astrology in newspapers.  From his interview with Ted Turner.

Also, photosets are fun.

I will never stop reblogging this set.

ohstarstuff:

New Interstellar Trailer
A third incredible trailer from Christopher Nolan’s new film “Interstellar” has been released. In the film, Matthew McConaughey plays an engineer who, along with several other scientists and astronauts, journeys through a newly discovered wormhole to save the world. The trailer features word’s from the beautiful Dylan Thomas poem “Night”.
Do not go gentle into that good night,Old age should burn and rave at close of day;Rage, rage against the dying of the light.
ohstarstuff:

New Interstellar Trailer
A third incredible trailer from Christopher Nolan’s new film “Interstellar” has been released. In the film, Matthew McConaughey plays an engineer who, along with several other scientists and astronauts, journeys through a newly discovered wormhole to save the world. The trailer features word’s from the beautiful Dylan Thomas poem “Night”.
Do not go gentle into that good night,Old age should burn and rave at close of day;Rage, rage against the dying of the light.
ohstarstuff:

New Interstellar Trailer
A third incredible trailer from Christopher Nolan’s new film “Interstellar” has been released. In the film, Matthew McConaughey plays an engineer who, along with several other scientists and astronauts, journeys through a newly discovered wormhole to save the world. The trailer features word’s from the beautiful Dylan Thomas poem “Night”.
Do not go gentle into that good night,Old age should burn and rave at close of day;Rage, rage against the dying of the light.

ohstarstuff:

New Interstellar Trailer


A third incredible trailer from Christopher Nolan’s new film “Interstellar” has been released. In the film, Matthew McConaughey plays an engineer who, along with several other scientists and astronauts, journeys through a newly discovered wormhole to save the world. The trailer features word’s from the beautiful Dylan Thomas poem “Night”.

Do not go gentle into that good night,
Old age should burn and rave at close of day;
Rage, rage against the dying of the light.

asapscience:

azuritereaction:

alexob:


AmoeBAND became a 2012 IDEA Award Finalist by innovating every possible aspect of the plaster (band aid).
The design revisions were:  
- Strategic cut-outs shape to fit fingers in such a way that it is easy to bend them and not disrupt the bandage.
- An intelligent dressing material allows you to regularly check wounds from the outside, without upsetting the healing process.“According to research, the when an infection of a wound is detected, the pH value is between 6.5 and 8.5. AmoeBAND’s indicator cross turns purple, alerting the user needs to change it immediately.”
- Since the bandage material used exudes a leather-like feel, availability in different skin-tones helps it blend in, without overly highlighting the injury.
- The packaging has been redesigned to a matchbox style and includes Braille instructions.
Hat tip to designers Tay Pek-Khai, Hsu Hao-Ming, Tsai Cheng-Yu, Chen Kuei-Yuan, Chen Yi-Ting, Lai Jen-Hao, Ho Chia-Ying, Chen Ying-shan, Weng Yu-Ching, and Chung Kuo-Ting


it’s always funny when people improve on something and you look at the innovations and it’s like so fucking obvious what needed to be changed, but yet no one seemingly thought of it until then, yourself included

^^^^^^^ high fives 
asapscience:

azuritereaction:

alexob:


AmoeBAND became a 2012 IDEA Award Finalist by innovating every possible aspect of the plaster (band aid).
The design revisions were:  
- Strategic cut-outs shape to fit fingers in such a way that it is easy to bend them and not disrupt the bandage.
- An intelligent dressing material allows you to regularly check wounds from the outside, without upsetting the healing process.“According to research, the when an infection of a wound is detected, the pH value is between 6.5 and 8.5. AmoeBAND’s indicator cross turns purple, alerting the user needs to change it immediately.”
- Since the bandage material used exudes a leather-like feel, availability in different skin-tones helps it blend in, without overly highlighting the injury.
- The packaging has been redesigned to a matchbox style and includes Braille instructions.
Hat tip to designers Tay Pek-Khai, Hsu Hao-Ming, Tsai Cheng-Yu, Chen Kuei-Yuan, Chen Yi-Ting, Lai Jen-Hao, Ho Chia-Ying, Chen Ying-shan, Weng Yu-Ching, and Chung Kuo-Ting


it’s always funny when people improve on something and you look at the innovations and it’s like so fucking obvious what needed to be changed, but yet no one seemingly thought of it until then, yourself included

^^^^^^^ high fives 
asapscience:

azuritereaction:

alexob:


AmoeBAND became a 2012 IDEA Award Finalist by innovating every possible aspect of the plaster (band aid).
The design revisions were:  
- Strategic cut-outs shape to fit fingers in such a way that it is easy to bend them and not disrupt the bandage.
- An intelligent dressing material allows you to regularly check wounds from the outside, without upsetting the healing process.“According to research, the when an infection of a wound is detected, the pH value is between 6.5 and 8.5. AmoeBAND’s indicator cross turns purple, alerting the user needs to change it immediately.”
- Since the bandage material used exudes a leather-like feel, availability in different skin-tones helps it blend in, without overly highlighting the injury.
- The packaging has been redesigned to a matchbox style and includes Braille instructions.
Hat tip to designers Tay Pek-Khai, Hsu Hao-Ming, Tsai Cheng-Yu, Chen Kuei-Yuan, Chen Yi-Ting, Lai Jen-Hao, Ho Chia-Ying, Chen Ying-shan, Weng Yu-Ching, and Chung Kuo-Ting


it’s always funny when people improve on something and you look at the innovations and it’s like so fucking obvious what needed to be changed, but yet no one seemingly thought of it until then, yourself included

^^^^^^^ high fives 
asapscience:

azuritereaction:

alexob:


AmoeBAND became a 2012 IDEA Award Finalist by innovating every possible aspect of the plaster (band aid).
The design revisions were:  
- Strategic cut-outs shape to fit fingers in such a way that it is easy to bend them and not disrupt the bandage.
- An intelligent dressing material allows you to regularly check wounds from the outside, without upsetting the healing process.“According to research, the when an infection of a wound is detected, the pH value is between 6.5 and 8.5. AmoeBAND’s indicator cross turns purple, alerting the user needs to change it immediately.”
- Since the bandage material used exudes a leather-like feel, availability in different skin-tones helps it blend in, without overly highlighting the injury.
- The packaging has been redesigned to a matchbox style and includes Braille instructions.
Hat tip to designers Tay Pek-Khai, Hsu Hao-Ming, Tsai Cheng-Yu, Chen Kuei-Yuan, Chen Yi-Ting, Lai Jen-Hao, Ho Chia-Ying, Chen Ying-shan, Weng Yu-Ching, and Chung Kuo-Ting


it’s always funny when people improve on something and you look at the innovations and it’s like so fucking obvious what needed to be changed, but yet no one seemingly thought of it until then, yourself included

^^^^^^^ high fives 

asapscience:

azuritereaction:

alexob:

AmoeBAND became a 2012 IDEA Award Finalist by innovating every possible aspect of the plaster (band aid).

The design revisions were:  

- Strategic cut-outs shape to fit fingers in such a way that it is easy to bend them and not disrupt the bandage.

- An intelligent dressing material allows you to regularly check wounds from the outside, without upsetting the healing process.“According to research, the when an infection of a wound is detected, the pH value is between 6.5 and 8.5. AmoeBAND’s indicator cross turns purple, alerting the user needs to change it immediately.

- Since the bandage material used exudes a leather-like feel, availability in different skin-tones helps it blend in, without overly highlighting the injury.

- The packaging has been redesigned to a matchbox style and includes Braille instructions.

Hat tip to designers Tay Pek-Khai, Hsu Hao-Ming, Tsai Cheng-Yu, Chen Kuei-Yuan, Chen Yi-Ting, Lai Jen-Hao, Ho Chia-Ying, Chen Ying-shan, Weng Yu-Ching, and Chung Kuo-Ting

it’s always funny when people improve on something and you look at the innovations and it’s like so fucking obvious what needed to be changed, but yet no one seemingly thought of it until then, yourself included

^^^^^^^ high fives 

Jupiter sound waves
Voyager recording

umhols:

vein:

neo-pvnk:

shining-suns:

beeblud:

This is the sound Jupiter emits via electromagnetic waves. It’s so incredibly cool (10:00)

it sounds so sad and lonely

It’s beautiful

home

holy fuck

So cool omg

coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery
coolthingsswd:

Ode to Apollo 11 and the joy of discovery

coolthingsswd:

Ode to Apollo 11 and the joy of discovery

scienceyoucanlove:

New laser surgery technique can turn your brown eyes blue

Of all the features we notice about a person upon meeting them, their eyes are often the first connection we make. But some people just aren’t satisfied with the color of their peepers, wishing their dark corneas away in favor of a pleasant shade of blue. Those unhappy with brown eyes may find just what they’re looking for: Laguna Beach doctor Gregg Homer has developed a new procedure that can actually convert brown-colored eyes to blue in just a matter of weeks.

The operation itself is fairly straight forward: Using a laser tuned to a special frequency, thedoctor actually alters the cells that produce the brown coloration in the eye. After a few weeks, the darker color begins to fade, revealing the blue pigment underneath. As the doctor explains it, the procedure only works for brown-eyed individuals, as they already have a bluish coloration hiding underneath.

According to Homer, the procedure takes just 20 seconds to complete. And because of the large number of people wishing they were born with baby blues, he has already been contacted by thousands of potential clients. Homer and his company, Stroma Medical, have been working on the technology for over a decade, and say it will be available on a consumer basis within three years.

He estimates the procedures will cost about $5,000 each, and as the brown coloration doesn’t appear to regenerate, your eyes should stay blue for the rest of your days. Unfortunately, that almost means it’s completely irreversible, so if you end up regretting a hasty decision to switch, you’ll never be brown-eyed again.

Not surprisingly, the practice has come under scrutiny by some who believe the color of our eyes is somehow more sacred than other parts of the human body — like the bits that plastic surgeons alter every day. There’s also the risk that long-term damage may result from the procedure, and without longitudinal research, Homer can’t guarantee that problems won’t arise down the road. Still, with would-be patients lining up by the thousands, it’s clear that some people believe the risk is worth the reward.

[Image Credit: Look into my eyes]

(Source)

This article originally appeared on Tecca

via Yahoo! tech news

koryos:

Dominance Behavior in Canids
I didn’t really even WANT to make a post about this.
The alpha-beta-omega model of wolf packs is dead in scientific literature, hammered into the ground, so to speak, and it’s been dead for over ten years. So why am I still hearing about it on TV and reading about it in articles? Why are popular dog trainers that encourage you to “be the alpha” still taken seriously?
I think the unfortunate truth is that the idea that there are strong and ferocious leaders in wolf packs and that you, too, can take on that role with your dog is just somehow appealing to people. Almost romantic, in the older sense of the word. And because of this, it makes money. It sells werewolf media. It sells dog training classes. Educational science channels that have no business promoting this false ideology keep it on board because it gets people watching.
If you couldn’t tell, I’m pretty fed up with the whole thing.
Okay, let’s talk about dominance, particularly what the word even means, because popular media does a terrible job of explaining it.
Read more…
koryos:

Dominance Behavior in Canids
I didn’t really even WANT to make a post about this.
The alpha-beta-omega model of wolf packs is dead in scientific literature, hammered into the ground, so to speak, and it’s been dead for over ten years. So why am I still hearing about it on TV and reading about it in articles? Why are popular dog trainers that encourage you to “be the alpha” still taken seriously?
I think the unfortunate truth is that the idea that there are strong and ferocious leaders in wolf packs and that you, too, can take on that role with your dog is just somehow appealing to people. Almost romantic, in the older sense of the word. And because of this, it makes money. It sells werewolf media. It sells dog training classes. Educational science channels that have no business promoting this false ideology keep it on board because it gets people watching.
If you couldn’t tell, I’m pretty fed up with the whole thing.
Okay, let’s talk about dominance, particularly what the word even means, because popular media does a terrible job of explaining it.
Read more…

koryos:

Dominance Behavior in Canids

I didn’t really even WANT to make a post about this.

The alpha-beta-omega model of wolf packs is dead in scientific literature, hammered into the ground, so to speak, and it’s been dead for over ten years. So why am I still hearing about it on TV and reading about it in articles? Why are popular dog trainers that encourage you to “be the alpha” still taken seriously?

I think the unfortunate truth is that the idea that there are strong and ferocious leaders in wolf packs and that you, too, can take on that role with your dog is just somehow appealing to people. Almost romantic, in the older sense of the word. And because of this, it makes money. It sells werewolf media. It sells dog training classes. Educational science channels that have no business promoting this false ideology keep it on board because it gets people watching.

If you couldn’t tell, I’m pretty fed up with the whole thing.

Okay, let’s talk about dominance, particularly what the word even means, because popular media does a terrible job of explaining it.

Read more…

thatscienceguy:

Stars are Huge Nuclear Explosions that are so large their own gravity keeps it in place.

image

pennyfornasa:

 
“To provide for research into problems of flight within and outside the earth’s atmosphere, and for other purposes.” - National Aeronautics and Space Act of 1958

On July 29th, 1958 — ten months after Sputnik 1 was launched into orbit — President Eisenhower signed the National Aeronautics and Space Act. Beginning operations later that year, NASA entered the highly competitive Space Race against the Soviet Union. Culminating with the success of Apollo, the economic benefits and technological advances during NASA’s first decade were immediately felt. Since 1958, twelve astronauts have walked on the Moon, four rovers and four landers have touched down on the Martian soil, and most recently, Voyager I became the first man-made object to enter interstellar space. Perhaps the greatest achievement of this agency, however, has been the success of the International Space Station. Astronauts from various space agencies across the planet have been living and studying aboard the ISS since 2000. NASA has had a rich history, but an even more promising future awaits.

Today, on the anniversary of the National Aeronautics and Space Act, join us by writing Congress to express the importance of raising the minuscule NASA budget to a level that will ensure a strong future for all humanity.

Sign the petition, spread the word:
www.penny4nasa.org/take-action

Read the National Aeronautics and Space Act:
http://history.nasa.gov/spaceact.html

mothernaturenetwork:

Scientists get first glimpse into workings of Higgs boson particles
What role do the Higgs bosons play in scattering and sticking to atoms?