Type of Spirals: A spiral is a curve in the plane or in the space, which runs around a centre in a special way.
Different spirals follow. Most of them are produced by formulas:The radius r(t) and the angle t are proportional for the simplest spiral, the spiral of Archimedes. Therefore the equation is:
(3) Polar equation: r(t) = at [a is constant].
From this follows
(2) Parameter form: x(t) = at cos(t), y(t) = at sin(t),
(1) Central equation: x²+y² = a²[arc tan (y/x)]².
You can make a spiral by two motions of a point: There is a uniform motion in a fixed direction and a motion in a circle with constant speed. Both motions start at the same point.
(1) The uniform motion on the left moves a point to the right. - There are nine snapshots.
(2) The motion with a constant angular velocity moves the point on a spiral at the same time. - There is a point every 8th turn.
(3) A spiral as a curve comes, if you draw the point at every turn(Image).
Figure 1: (1) Archimedean spiral - (2) Equiangular Spiral (Logarithmic Spiral, Bernoulli’s Spiral).
Figure 2 : (1) Clothoide (Cornu Spiral) - (2) Golden spiral (Fibonacci number).
More Spirals: If you replace the term r(t)=at of the Archimedean spiral by other terms, you get a number of new spirals. There are six spirals, which you can describe with the functions f(x)=x^a [a=2,1/2,-1/2,-1] and f(x)=exp(x), f(x)=ln(x). You distinguish two groups depending on how the parameter t grows from 0.
Figure 4: If the absolute modulus of a function r(t) is increasing, the spirals run from inside to outside and go above all limits. The spiral 1 is called parabolic spiral or Fermat’s spiral.
Figure 5: If the absolute modulus of a function r(t) is decreasing, the spirals run from outside to inside. They generally run to the centre, but they don’t reach it. There is a pole. Spiral 2 is called the Lituus (crooked staff).
Figure 7: Spirals Made of Line Segments.
Source: Spirals by Jürgen Köller.
See more on Wikipedia: Spiral, Archimedean spiral, Cornu spiral, Fermat’s spiral, Hyperbolic spiral, Lituus, Logarithmic spiral,
Fibonacci spiral, Golden spiral, Rhumb line, Ulam spiral,
Hermann Heights Monument, Hermannsdenkmal.
The famous theoretical physicist John Archibald Wheeler coined the term “It from Bit”. He says that ”It” — every particle, every field of force, even the space-time continuum itself — derives its function, its meaning, its very existence entirely — even if in some contexts indirectly — from the apparatus-elicited answers to yes-or-no questions, binary choices, “bits.” This concept symbolizes the idea that every item of the physical world has at bottom — a very deep bottom, in most instances — an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-or-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe.
Wheeler speculated that we are part of a universe that is a work in progress; we are tiny patches of the universe looking at itself — and building itself. It’s not only the future that is still undetermined but the past as well. And by peering back into time, even all the way back to the Big Bang, our present observations select one out of many possible quantum histories for the universe.
At every moment, in Wheeler’s view, the entire universe is filled with events, where the possible outcomes of countless interactions become real, where the infinite variety inherent in quantum mechanics manifests as a physical cosmos. And we see only a tiny portion of that cosmos. Wheeler suspected that most of the universe consists of huge clouds of uncertainty that have not yet interacted either with a conscious observer or even with some lump of inanimate matter. He sees the universe as a vast arena containing realms where the past is not yet fixed.
The most important scientific revolutions all include, as their only common feature, the dethronement of human arrogance from one pedestal after another of previous convictions about our centrality in the cosmos.– Stephen Jay Gould (via laboratoryequipment) Via Birds on the Brain
The Goldbach Conjecture
The Goldbach Conjecture states that every even number greater than two is the sum of two prime numbers. This cool diagram demonstrates this for every even number from four to fifty. The conjecture was first proposed in 1742 and while it is widely considered to be true, it has yet to be proven.
HIV-1, the most common type of the virus that causes AIDS,has proved to be tenacious, inserting its genome permanently into its victims’ DNA, forcing patients to take a lifelong drug regimen to control the virus and prevent a fresh attack. Now, a team of Temple University School of Medicine researchers has designed a way to snip out the integrated HIV-1 genes for good.
"This is one important step on the path toward a permanent cure for AIDS," says Kamel Khalili, PhD, Professor and Chair of the Department of Neuroscience at Temple. Khalili and his colleague, Wenhui Hu, MD, PhD, Associate Professor of Neuroscience at Temple, led the work which marks the first successful attempt to eliminate latent HIV-1 virus from human cells. "It’s an exciting discovery, but it’s not yet ready to go into the clinic. It’s a proof of concept that we’re moving in the right direction," added Dr. Khalili, who is also Director of the Center for Neurovirology and Director of the Comprehensive NeuroAIDS Center at Temple.
In a study published July 21 by theProceedings of the National Academy of Sciences, Khalili and colleagues detail how they created molecular tools to delete the HIV-1 proviral DNA. When deployed, a combination of a DNA-snipping enzyme called a nuclease and a targeting strand of RNA called a guide RNA (gRNA) hunt down the viral genome and excise the HIV-1 DNA. From there, the cell’s gene repair machinery takes over, soldering the loose ends of the genome back together — resulting in virus-free cells.
"Since HIV-1 is never cleared by the immune system, removal of the virus is required in order to cure the disease," says Khalili, whose research focuses on the neuropathogenesis of viral infections. The same technique could theoretically be used against a variety of viruses, he says.
A look today at the chemicals behind insect repelling sprays.
Read more here, including a possible reason why mosquitos just prefer some people more than others: http://wp.me/p4aPLT-mS
Image: Courtney White
What is the best way to utilize sunlight—to grow food or to produce fuel?
For millennia, the answer was easy: we used solar energy to grow plants that we could eat. Then, in the 1970s, the answer became more complex as fields of photovoltaic panels (PVPs) began popping up all over the planet, sometimes on former farmland. In the 1990s, farmers began growing food crops for fuels such as corn-based ethanol. The problem is that the food-fuel equation has become a zero-sum game.
That led French agricultural scientist Christian Dupraz to ponder whether both food and fuel production could be successfully combined on one plot of land. For example, why not build solar panels above a farm field so that electricity and food can be produced simultaneously? In addition to resolving the conflict between land uses, solar panels would provide an additional source of income to farmers while at the same time sheltering crops from the rising temperatures and destructive hail and rain storms associated with climate change.
In 2010, Dupraz and his colleagues at INRA, France’s agricultural research institute, built the first-ever “agrivoltaic” farm, near Montpellier. In an 860-square-meter field, they planted crops in four adjacent plots—two in full sun as controls, one under a standard-density array of PVPs, and one under a half-density array of PVPs.
The researchers assumed crop productivity would decline in the shade, since plants would have to compete with solar panels for radiation and possibly water. But they also wondered whether, in a warming world, shade might actually improve crop productivity. “Shade will reduce transpiration needs and possibly increase water efficiency,” Dupraz wrote. The key would be finding the right balance between electricity produced by the solar panels and productive capacity of the farm.
At the end of three growing seasons, the researchers found that compromise was indeed possible. Not surprisingly, the crops under the full-density PVP shading lost nearly 50 percent of their productivity, compared to similar crops in the full-sun plots. However, the crops under the half-density shading were just as productive as the ones in the unshaded control plots; in a few cases, they were even more productive. (1)
The reason for this surprising outcome, according to Hélène Marrou, who studied lettuce in the plots, was the ability of plants to adapt to lower light conditions. She reported that lettuce plants adjusted by increasing their leaf area and by altering leaf arrangement to harvest light more efficiently.
She also had good news to report on the water front. “We showed in this experiment that shading irrigated vegetable crops with PVPs allowed a saving of 14 percent to 29 percent of evapotranspired water, depending on the level of shade created and the crop grown,” she wrote in a 2013 paper. (2) Within the context of global warming and water shortage, she said, reducing water demand by shading plants could represent a big advantage in the near future.
Ocean Floor Mats Send Power to the Surface
“A wave power technology called M3 Wave dispenses with all the problems that come with buoys or other above- and below-the-surface designs by mooring a simple device to the ocean floor. The device contains two air chambers connected by a wind tunnel of sorts. As a wave passes over the top of the first chamber, the pressure inside increases—forcing air through a passageway to the second chamber. Inside the passageway is a turbine, so the passing air is actually what generates the electricity. As the wave continues on, it raises the pressure inside the second chamber, pushing the air back through the turbine and into the first chamber (the turbine is bidirectional). Another wave, another cycle. Repeat.”
Learn more from Conservation Magazine.
Harnessing the power of the oceans….