unexplained-events:

Negatives discovered in an exploration hut in Antarctica, which had been abandoned for nearly 100 years, were found and processed. The images give a ghostly look into the past, during the “heroic era” of Antarctic exploration.

spaceplasma:

On August 24th at 12:17 UT, NASA’s Solar Dynamics Observatory recorded this M5.6-category explosion near the eastern limb of the sun.

The source of the blast was sunspot AR2151. As the movie shows, an instability in the suspot’s magnetic canopy hurled a dense plume of plasma into space. If that plasma cloud were to hit Earth, the likely result would be strong geomagnetic storms. However, because of the sunspot’s location near the edge of the solar disk, Earth was not in the line of fire.

Even so, the flare did produce some Earth effects. A pulse of extreme UV radiation from the explosion partially ionized our planet’s upper atmosphere, resulting in a Sudden Ionospheric Disturbance (SID). Waves of ionization altered the normal propagation of VLF (very low frequency) radio transmissions over the the dayside of Earth, an effect recorded at the Polarlightcenter in Lofoten, Norway: data.

Credit: NASA/SDO

chand3li3r-0f-th3-n3t:

sixpenceee:

THERE’S A MAN IN THE WOODS
Another great short film, only 3 minutes long that takes a dark turn. You might even sympathize with the man in the woods. 
WATCH IT HERE
CREEPY SHORT FILMS COMPILATION

I…actually stopped breathing near the middle part..HOLY SHIT WHAAAAAAAATTT?!?!?!?!?!

chand3li3r-0f-th3-n3t:

sixpenceee:

THERE’S A MAN IN THE WOODS

Another great short film, only 3 minutes long that takes a dark turn. You might even sympathize with the man in the woods. 

WATCH IT HERE

CREEPY SHORT FILMS COMPILATION

I…actually stopped breathing near the middle part..
HOLY SHIT WHAAAAAAAATTT?!?!?!?!?!

randommarius:

Archimedes and the quadrature of the parabolaArchimedes of Syracuse (c. 287–212 BC) was a Greek mathematician, scientist and engineer. He is widely regarded as one of the greatest mathematicians of all time.One of Archimedes’ works was called The Quadrature of the Parabola. This proved various results about parabolas, and explained how to find the area of a parabolic segment, which is a finite region enclosed by a parabola and a line. This is easy to do nowadays using the well-known theory of integral calculus, but this was not developed until the 17th century, about 1900 years after the time of Archimedes.Integral calculus calculates areas by approximating the area to be measured by a union of geometric shapes whose exact areas are known, and then applying a limiting process. Archimedes’ technique was very similar to this. The key to his idea was to inscribe into the parabolic segment a triangle with the same base and height. In other words, the triangle had the original line segment as its base, and touched the curved part of the parabola at the point where the tangent line to the parabola was parallel to the line segment. Archimedes proved that if the triangle has area T, then the area A of the parabolic segment was given by 4T/3.Archimedes described a method of filling up the rest of the parabolic segment by exhaustion, using smaller and smaller triangles. The graphic shows two lighter blue triangles, four yellow triangles, eight (barely visible) red triangles, and so on. There are twice as many triangles of each successive colour as there were of the previous colour. Archimedes proved that the area of a triangle of each successive colour is 1/8 of the area of the previous type of triangle, although this is not an obvious result. For example, each light blue triangle has an area of T/8.These observations reduce the problem of finding the area A to evaluating the sum at the bottom of the picture, which is a geometric series. Nowadays, there is a well-known formula that applies in this situation, but Archimedes summed the series using a clever ad hoc geometric argument instead.Archimedes made some other very significant discoveries using integration-like methods. He proved that the area of a circle of radius r is equal to πr^2, and he also discovered the formulae for the surface area and volume of a sphere, and for the volume and area of a cone. Archimedes is also known for inventing the Claw of Archimedes and the Archimedes heat ray, both of which were weapons to defend the city of Syracuse. The claw was a kind of mobile grappling hook that could lift enemy ships out of the water, and modern experiments suggest that this would have been a workable device. The heat ray was a system of mirrors to focus reflected sunlight on to enemy ships, thus setting them on fire. Modern attempts to reproduce the heat ray have concluded that it would not have worked quickly enough in typical weather conditions to be able to burn enemy ships.Relevant linksWikipedia on Archimedes: http://en.wikipedia.org/wiki/ArchimedesWikipedia on The Quadrature of the Parabola (including the graphic here): http://en.wikipedia.org/wiki/The_Quadrature_of_the_ParabolaPicture of Archimedes from http://totallyhistory.com/archimedes/I stole the joke in the picture from Dan McQuillan on Twitter.Here’s another good joke about Newton and Leibniz developing calculus in the 17th century, which someone in my department has on their office door: http://xkcd.com/626/ #mathematics   #sciencesundayhttp://click-to-read-mo.re/p/95IQ/53e952d4

randommarius:

Archimedes and the quadrature of the parabola

Archimedes of Syracuse (c. 287–212 BC) was a Greek mathematician, scientist and engineer. He is widely regarded as one of the greatest mathematicians of all time.

One of Archimedes’ works was called The Quadrature of the Parabola. This proved various results about parabolas, and explained how to find the area of a parabolic segment, which is a finite region enclosed by a parabola and a line. This is easy to do nowadays using the well-known theory of integral calculus, but this was not developed until the 17th century, about 1900 years after the time of Archimedes.

Integral calculus calculates areas by approximating the area to be measured by a union of geometric shapes whose exact areas are known, and then applying a limiting process. Archimedes’ technique was very similar to this. The key to his idea was to inscribe into the parabolic segment a triangle with the same base and height. In other words, the triangle had the original line segment as its base, and touched the curved part of the parabola at the point where the tangent line to the parabola was parallel to the line segment. Archimedes proved that if the triangle has area T, then the area A of the parabolic segment was given by 4T/3.

Archimedes described a method of filling up the rest of the parabolic segment by exhaustion, using smaller and smaller triangles. The graphic shows two lighter blue triangles, four yellow triangles, eight (barely visible) red triangles, and so on. There are twice as many triangles of each successive colour as there were of the previous colour. Archimedes proved that the area of a triangle of each successive colour is 1/8 of the area of the previous type of triangle, although this is not an obvious result. For example, each light blue triangle has an area of T/8.

These observations reduce the problem of finding the area A to evaluating the sum at the bottom of the picture, which is a geometric series. Nowadays, there is a well-known formula that applies in this situation, but Archimedes summed the series using a clever ad hoc geometric argument instead.

Archimedes made some other very significant discoveries using integration-like methods. He proved that the area of a circle of radius r is equal to πr^2, and he also discovered the formulae for the surface area and volume of a sphere, and for the volume and area of a cone. Archimedes is also known for inventing the Claw of Archimedes and the Archimedes heat ray, both of which were weapons to defend the city of Syracuse. The claw was a kind of mobile grappling hook that could lift enemy ships out of the water, and modern experiments suggest that this would have been a workable device. The heat ray was a system of mirrors to focus reflected sunlight on to enemy ships, thus setting them on fire. Modern attempts to reproduce the heat ray have concluded that it would not have worked quickly enough in typical weather conditions to be able to burn enemy ships.

Relevant links
Wikipedia on Archimedes: http://en.wikipedia.org/wiki/Archimedes

Wikipedia on The Quadrature of the Parabola (including the graphic here): http://en.wikipedia.org/wiki/The_Quadrature_of_the_Parabola

Picture of Archimedes from http://totallyhistory.com/archimedes/

I stole the joke in the picture from Dan McQuillan on Twitter.

Here’s another good joke about Newton and Leibniz developing calculus in the 17th century, which someone in my department has on their office door: http://xkcd.com/626/

#mathematics   #sciencesunday

http://click-to-read-mo.re/p/95IQ/53e952d4