iwanttoberecycled

iwanttoberecycled:

archiemcphee:

Instructables play editor and community manager Mike Warren created a tutorial for transforming plastic toy animals into awesome corn cob holders. Mike even cleverly designed his holders to firmly reconnect, so they can also be displayed as cute toys when they aren’t in use.

Click here for Mike’s tutorial.

I want to be holding it all together. 

spring-of-mathematics
fouriestseries:

Gabriel’s Horn and the Painter’s Paradox 
Gabriel’s Horn is a three-dimensional horn shape with the counterintuitive property of having a finite volume but an infinite surface area.
This fact results in the Painter’s Paradox — A painter could fill the horn with a finite quantity of paint, “and yet that paint would not be sufficient to coat [the horn’s] inner surface” [1].
If the horn’s bell had, for example, a 6-inch radius, we’d only need about a half gallon of paint to fill the horn all the way up. Even though this half gallon is enough to entirely fill the horn, it’s not enough to even coat a fraction of the inner wall!
The mathematical explanation is a bit confusing if you haven’t taken a first course in calculus, but if you’re interested, you can check it out here.
Mathematica code:
x[u_, v_] := u
y[u_, v_] := Cos[v]/u
z[u_, v_] := Sin[v]/u
Manipulate[ParametricPlot3D[{{x[u, v], y[u, v], z[u, v]}}, 
    {u, 1, umax}, {v, 0, 2*Pi}, 
    PlotRange -> {{0, 20}, {-1, 1}, {-1, 1}}, 
    Mesh -> {Floor[umax], 20}, Axes -> False, Boxed -> False], 
    {{umax, 20}, 1.1, 20}]
Additional source not linked above.

fouriestseries:

Gabriel’s Horn and the Painter’s Paradox 

Gabriel’s Horn is a three-dimensional horn shape with the counterintuitive property of having a finite volume but an infinite surface area.

This fact results in the Painter’s Paradox — A painter could fill the horn with a finite quantity of paint, “and yet that paint would not be sufficient to coat [the horn’s] inner surface” [1].

If the horn’s bell had, for example, a 6-inch radius, we’d only need about a half gallon of paint to fill the horn all the way up. Even though this half gallon is enough to entirely fill the horn, it’s not enough to even coat a fraction of the inner wall!

The mathematical explanation is a bit confusing if you haven’t taken a first course in calculus, but if you’re interested, you can check it out here.

Mathematica code:

x[u_, v_] := u
y[u_, v_] := Cos[v]/u
z[u_, v_] := Sin[v]/u
Manipulate[ParametricPlot3D[{{x[u, v], y[u, v], z[u, v]}}, 
    {u, 1, umax}, {v, 0, 2*Pi}, 
    PlotRange -> {{0, 20}, {-1, 1}, {-1, 1}}, 
    Mesh -> {Floor[umax], 20}, Axes -> False, Boxed -> False], 
    {{umax, 20}, 1.1, 20}]

Additional source not linked above.

neuromorphogenesis
neuromorphogenesis:

What Happens If You Apply Electricity to the Brain of a Corpse?
Some habits die hard. Like humans zapping their brains. We did this back in Ancient Greece, when medics used electric fish to treat headaches and other ailments. Today we’re still at it, as neuroscientists apply electric currents to people’s brains to boost their mental function, treat depression, or give them lucid dreams.
Subjecting the brain to external electricity has an influence on mental function because our neurons communicate with each other using electricity and chemicals. This has become relatively common knowledge today, but only two centuries ago scientists were still quite baffled by the mystery of nerve communication.
Issac Newton and others suggested that our nerves communicate with each other, and with the muscles, via vibrations. Another suggestion of the time was that the nerves emit some kind of fluid. Most opaque, and still popular, was the idea – first mooted in ancient times – that the brain and nerves are filled with mysterious “animal spirits”.
“Animal electricity”
During the eighteenth century our understanding of electricity was growing apace, and the use of electricity to treat a range of physical and mental ailments, known as electrotherapy, was incredibly popular. But still it wasn’t obvious to scientists at the time that the human nervous system produces its own electric charge, and that the nerves communicate using electricity.
Among the first scientists to make this proposal was the Italian physician Luigi Galvani (1737-1798). Most of Galvani’s experiments were with frogs’ legs and nerves, and he was able to show that lightning or man-made electrical machines could cause the frogs’ muscles to twitch. He subsequently came up with the idea of “animal electricity” – that animals, humans included, have their own intrinsic electricity.
“I believe it has been sufficiently well established that there is present in animals an electricity which we … are wont to designate with the general term ‘animal’ … “ he wrote. “It is seen most clearly … in the muscles and nerves.”
Neuroscience’s macabre past
However, to Galvani’s frustration, he failed to show that zapping the brain had an effect on the facial or peripheral muscles. Here, he was helped in dramatic, macabre fashion by his nephew Giovanni Aldini (1762-1834).
In 1802, Aldini zapped the brain of a decapitated criminal by placing a metal wire into each ear and then flicking the switch on the attached rudimentary battery. “I initially observed strong contractions in all the muscles of the face, which were contorted so irregularly that they imitated the most hideous grimaces,” he wrote in his notes. “The action of the eylids was particularly marked, though less striking in the human head than in that of the ox.”
During this era, there was fierce scientific debate about the role of electricity in human and animal nervous systems. Galvani’s influential rival, Alessandro Volta, for one, did not believe in the notion that animals produce their own electricity. In this context, the rival camps engaged in public relations exercises to promote their own views. This played to Aldini’s strengths. Something of a showman, he took his macabre experiments on tour. In 1803, he performed a sensational public demonstration at the Royal College of Surgeons, London, using the dead body of Thomas Forster, a murderer recently executed by hanging at Newgate. Aldini inserted conducting rods into the deceased man’s mouth, ear, and anus.
One member of the large audience later observed: “On the first application of the process to the face, the jaw of the deceased criminal began to quiver, the adjoining muscles were horribly contorted, and one eye was actually opened. In the subsequent part of the process, the right hand was raised and clenched, and the legs and thighs were set in motion. It appeared to the uninformed part of the bystanders as if the wretched man was on the eve of being restored to life.”
Although Frankenstein author Mary Shelley was only five when this widely reported demonstration was performed, it’s obvious that she was inspired by contemporary scientific debates about electricity and the human body. Indeed, publication of her novel coincided with another dramatic public demonstration performed in 1818 in Glasgow by Andrew Ure, in which application of electric current to a corpse appeared to cause it to resume heavy breathing, and even to point its fingers at the audience.
Death is a process
If a body is dead, how come its nerves are still responsive to external electric charge? In 1818, one popular but mistaken suggestion was that electricity is the life force, and that the application of electricity to the dead could literally bring them back to life. Indeed, so disturbed were many members of the audience at Ure’s demonstration that they had to leave the building. One man reportedly fainted. Modern scientific understanding of the way nerves communicate undermines such supernatural interpretations, but you can imagine that witnessing such a spectacle as performed by Ure or Aldini would even today be extremely unnerving (excuse the pun). A pithy explanation of why electricity appears to animate a dead body comes courtesy of Frances Ashcroft’s wonderful book The Spark of Life:
“The cells of the body do not die when an animal (or person) breathes its last breath, which is why it is possible to transplant organs from one individual to another, and why blood transfusions work,” she writes. “Unless it is blown to smithereens, the death of a multicellular organism is rarely an instantaneous event, but instead a gradual closing down, an extinction by stages. Nerve and muscle cells continue to retain their hold on life for some time after the individual is dead and thus can be ‘animated’ by application of electricity.”
The grisly experiments of Aldini and Ure seem distasteful by today’s standards, but they were historically important, stimulating the imagination of novelists and scientists alike.

neuromorphogenesis:

What Happens If You Apply Electricity to the Brain of a Corpse?

Some habits die hard. Like humans zapping their brains. We did this back in Ancient Greece, when medics used electric fish to treat headaches and other ailments. Today we’re still at it, as neuroscientists apply electric currents to people’s brains to boost their mental function, treat depression, or give them lucid dreams.

Subjecting the brain to external electricity has an influence on mental function because our neurons communicate with each other using electricity and chemicals. This has become relatively common knowledge today, but only two centuries ago scientists were still quite baffled by the mystery of nerve communication.

Issac Newton and others suggested that our nerves communicate with each other, and with the muscles, via vibrations. Another suggestion of the time was that the nerves emit some kind of fluid. Most opaque, and still popular, was the idea – first mooted in ancient times – that the brain and nerves are filled with mysterious “animal spirits”.

“Animal electricity”

During the eighteenth century our understanding of electricity was growing apace, and the use of electricity to treat a range of physical and mental ailments, known as electrotherapy, was incredibly popular. But still it wasn’t obvious to scientists at the time that the human nervous system produces its own electric charge, and that the nerves communicate using electricity.

Among the first scientists to make this proposal was the Italian physician Luigi Galvani (1737-1798). Most of Galvani’s experiments were with frogs’ legs and nerves, and he was able to show that lightning or man-made electrical machines could cause the frogs’ muscles to twitch. He subsequently came up with the idea of “animal electricity” – that animals, humans included, have their own intrinsic electricity.

“I believe it has been sufficiently well established that there is present in animals an electricity which we are wont to designate with the general term ‘animal’ “ he wrote. “It is seen most clearly in the muscles and nerves.”

Neuroscience’s macabre past

However, to Galvani’s frustration, he failed to show that zapping the brain had an effect on the facial or peripheral muscles. Here, he was helped in dramatic, macabre fashion by his nephew Giovanni Aldini (1762-1834).

In 1802, Aldini zapped the brain of a decapitated criminal by placing a metal wire into each ear and then flicking the switch on the attached rudimentary battery. “I initially observed strong contractions in all the muscles of the face, which were contorted so irregularly that they imitated the most hideous grimaces,” he wrote in his notes. “The action of the eylids was particularly marked, though less striking in the human head than in that of the ox.”

During this era, there was fierce scientific debate about the role of electricity in human and animal nervous systems. Galvani’s influential rival, Alessandro Volta, for one, did not believe in the notion that animals produce their own electricity. In this context, the rival camps engaged in public relations exercises to promote their own views. This played to Aldini’s strengths. Something of a showman, he took his macabre experiments on tour. In 1803, he performed a sensational public demonstration at the Royal College of Surgeons, London, using the dead body of Thomas Forster, a murderer recently executed by hanging at Newgate. Aldini inserted conducting rods into the deceased man’s mouth, ear, and anus.

One member of the large audience later observed: “On the first application of the process to the face, the jaw of the deceased criminal began to quiver, the adjoining muscles were horribly contorted, and one eye was actually opened. In the subsequent part of the process, the right hand was raised and clenched, and the legs and thighs were set in motion. It appeared to the uninformed part of the bystanders as if the wretched man was on the eve of being restored to life.”

Although Frankenstein author Mary Shelley was only five when this widely reported demonstration was performed, it’s obvious that she was inspired by contemporary scientific debates about electricity and the human body. Indeed, publication of her novel coincided with another dramatic public demonstration performed in 1818 in Glasgow by Andrew Ure, in which application of electric current to a corpse appeared to cause it to resume heavy breathing, and even to point its fingers at the audience.

Death is a process

If a body is dead, how come its nerves are still responsive to external electric charge? In 1818, one popular but mistaken suggestion was that electricity is the life force, and that the application of electricity to the dead could literally bring them back to life. Indeed, so disturbed were many members of the audience at Ure’s demonstration that they had to leave the building. One man reportedly fainted. Modern scientific understanding of the way nerves communicate undermines such supernatural interpretations, but you can imagine that witnessing such a spectacle as performed by Ure or Aldini would even today be extremely unnerving (excuse the pun). A pithy explanation of why electricity appears to animate a dead body comes courtesy of Frances Ashcroft’s wonderful book The Spark of Life:

“The cells of the body do not die when an animal (or person) breathes its last breath, which is why it is possible to transplant organs from one individual to another, and why blood transfusions work,” she writes. “Unless it is blown to smithereens, the death of a multicellular organism is rarely an instantaneous event, but instead a gradual closing down, an extinction by stages. Nerve and muscle cells continue to retain their hold on life for some time after the individual is dead and thus can be ‘animated’ by application of electricity.”

The grisly experiments of Aldini and Ure seem distasteful by today’s standards, but they were historically important, stimulating the imagination of novelists and scientists alike.

spring-of-mathematics

spring-of-mathematics:

Reconsidering time: Linear Cycle Clock & Spiral of Theodorus in Mathematics:

Linear Cycle Clock & Ideas: Exploring the concept of time continues to fascinate designers. Like Uji by Fabrica, the Linear Cycle from BCXSY is not a common clock. Instead of the usual rotating dials, the clock features a revolving element that shows the passing of time on a linear plate instead of a circular one - Source: Commissioned by Isabelle Daëron and Fabien Petiot for Roues Libres (Freewheel) for D’Days 2014 in Paris, this unique time display offers an alternative to the ordinary clock and makes us consider how we advance through time.

Spiral of Theodorus & Construction: In geometry, the spiral of Theodorus (also called square root spiral, Einstein spiral or Pythagorean spiral) is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene.
The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed, an automedian right triangle with one leg being the hypotenuse of the prior triangle (with length √2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is √3. The process then repeats; the i th triangle in the sequence is a right triangle with side lengths √i and 1, and with hypotenuse √i + 1. For example, the 16th triangle has sides measuring 4 (=√16), 1 and hypotenuse of √17.

Images: Spiral of Theodorus on Wikipedia & The article: Spiral of Theodorus by Elizabeth Nelli on Jwilson.coe.uga.edu.