The system for measuring temperature on a decimal scale was introduced by Anders Celsius, a Swedish astronomer with many accomplishments in a short life. The Celsius scale was originally called the centigrade scale, from the Latin words centus for one hundred and gradus meaning degree. The eponym Celsius wasn’t adopted by the scientific community until 1948 and remains the only scientific symbol in the upper case (°C), to distinguish it from the lower case c (constant) famous from Einstein’s energy equation.
Despite his obvious genius, the centigrade scale originally proposed by Anders Celsius had 100 as the freezing point of water and 0 as the boiling point. In 1744 and shortly after his death, the great Swedish scientist Carl Linneaus reversed the scale making hot temperatures have higher numbers than cold temperatures.
Today the Celsius scale is the most widely used scale for measuring and reporting temperature. In addition to his interest in a better scale for measuring temperature, Anders Celsius participated in expeditions to confirm Isaac Newton’s theory that the Earth is not a perfect sphere but rather ellipsoid, and also was the first to use colored glass plates to try to analyse and catalog magnitude and differences in stars. He supported the formation of the Royal Swedish Academy of Sciences (along with Carl Linneaus and several others) and was elected to the Academy in its first meeting. He died of tuberculosis in 1744 at the age of 42.
Image of Anders Celsius from the portrait that hangs in his honor at the Uppsala Astronomical Observatory which he founded shortly before his death. Image in the public domain.
via kidsneedscience
The Complex Structure of Bucket Orchids
Orchids of the genus Coryanthes have evolved along with orchid bees, and depend on each other for reproduction.
Male bees are attracted to an pheromone laced wax produced under the orchid’s helmet. The wax is stored by the male and are used in courtship. However, the helmet is slippery and bees sometimes fall into the fluid filled bucket below.
Once in the bucket, their wings are wet, which prevent them from flying. The walls of the bucket are smooth and lined with downward pointing hairs, preventing the insect from escaping through climbing. A small opening towards the front of the flower is the only way out.
As the bee climbs through the narrow opening, they must press their bodies against sticky pollen packets. These are essentially glued to the bee’s body as it tries to escape. In order for fertilisation to happen, the pollen from one plant must be transferred to the stigma of another plant.
After the bee flies off and visits another flower, it goes through a similar ordeal. This time, as it exits the bucket, the pollen packet on its back brushes past the stigma of the new flower, thus achieving pollination.
dwittkower, dogtooth77, Alex Popovkin on Flickr
via ichthyologist
A humbling map of real-time wind patterns in Tornado Alley
“Wind Map” is a stunning interactive data visualization that presents wind patterns across the continental U.S. in real time. Picture above is what it looked like last night at 10:59 CDT, in the aftermath of yesterday’s devastating Oklahoma tornado.”
Read more here from io9.
via kqedscience
An even number of (at least 8) tetrahedra can be connected along their edges to form a ring in a way that allows them to be continuously rotated “inside-out” without disconnecting. Such configurations are commonly referred to as kaleidocycles. Shown above are kaleidocycles with 8, 10, and 12 tetrahedra exhibiting 4, 5, and 6-fold rotational symmetry, respectively. There has to be at least 8 tetrahedra, because any less would result in the tetrahedra colliding into each other at certain instances of the rotation. You can even make your own paper model using this guide.
Mathematica code:
v1[t_] :=
{Cos[t], 0, Sin[t]}
v2[t_, a_] :=
1/Sqrt[1 + Sin[t]^2 Tan[a]^2] {-Sin[t], -Sin[t] Tan[a], Cos[t]}
v3[t_, a_] :=
1/Sqrt[1 + Sin[t]^2 Tan[a]^2] {-Sin[t]^2 Tan[a], 1, Cos[t] Sin[t] Tan[a]}
P[t_, a_] :=
{v3[t, a][[2]]/Tan[a] - v3[t, a][[1]], 0, -v3[t, a][[3]]/2}
Q[t_, a_] :=
{v3[t, a][[2]]/Tan[a], v3[t, a][[2]], v3[t, a][[3]]/2}
vertices[t_, a_] :=
{P[t, a] - Sqrt[2]/2 v1[t], P[t, a] + Sqrt[2]/2 v1[t],
Q[t, a] - Sqrt[2]/2 v2[t, a], Q[t, a] + Sqrt[2]/2 v2[t, a]}
Tetrahedron[T_, t_, a_, o_] :=
Table[
{FaceForm[White], Opacity[o], EdgeForm[Thick],
Polygon[
Table[
T[vertices[t, a][[1 + Mod[i + j, 4]]]], {i, 1, 3, 1}]]},
{j, 0, 3, 1}]
Kaleidocycle[pr_, t_, n_, o_, A_] := Graphics3D[
Rotate[
Table[
Rotate[
Table[
Tetrahedron[T, t, 2 Pi/n, o],
{T, {TransformationFunction[IdentityMatrix[4]],
ReflectionTransform[{-Sin[2 Pi/n], Cos[2 Pi/n], 0}]}}],
r*4 Pi/n, {0, 0, 1}],
{r, 0, n - 1, 1}],
A*Sin[t], {0, 1, 0}],
PlotRange -> pr, ImageSize -> 500, Axes -> False, Boxed -> False,
Lighting -> "Neutral", ViewPoint -> {0, 0, 2}, Background -> White ]
Manipulate[
Kaleidocycle[pr, t, n, o, A],
{pr, 1.5, 50}, {t, 0, 2 Pi}, {n, 8, 16, 1},{o, 1, 0}, {{A, 0}, 0, 2 Pi}]
via intothecontinuum
![matthen:
If a mathematician wants to cross a road, they will think carefully about their optimal path. The total distance of the path should be minimised, but they prefer walking on the sidewalk to the road. If there is no extra discomfort from being on the road, the best path is a straight line, but as it increases it is better to cross the road more directly. The resulting path is exactly the same as a ray of light refracting through a block of glass [with relative refractive index equal to the ratio of these ‘discomfort levels’]. Fermat’s principle says that light will want to spend less time in the glass (on the road), as it actually travels more slowly in the glass. [video] [code] [more]](http://25.media.tumblr.com/df2ee0f76e2abdae3c4365777fad278a/tumblr_mn3pdz8I7f1qfg7o3o1_400.gif)
If a mathematician wants to cross a road, they will think carefully about their optimal path. The total distance of the path should be minimised, but they prefer walking on the sidewalk to the road. If there is no extra discomfort from being on the road, the best path is a straight line, but as it increases it is better to cross the road more directly. The resulting path is exactly the same as a ray of light refracting through a block of glass [with relative refractive index equal to the ratio of these ‘discomfort levels’]. Fermat’s principle says that light will want to spend less time in the glass (on the road), as it actually travels more slowly in the glass. [video] [code] [more]
via matthen
Goldbach Variations | Roots of Unity, Scientific American Blog Network:
On Monday, Harald Helfgott of the École Normale Supériure in Paris posted a proof of one of the oldest open problems in number theory to the preprint repository arxiv. The ternary Goldbach conjecture, like so many questions in number theory, is easy to state but hard to prove. Every odd number greater than 5 can be written as the sum of three prime numbers. (Prime numbers have no factors other than themselves and the number 1.) For example, 7=2+2+3 and 91=7+41+43.
The ternary Goldbach conjecture is sometimes called the weak Goldbach conjecture. The strong Goldbach conjecture states that every even number greater than 2 can be written as the sum of two primes. Both conjectures were formulated in correspondence between Christian Goldbach and Leonhard Euler in 1742, hence the name. Logically enough, if you prove the strong Goldbach conjecture, you get the weak one for free: if you have an odd number greater than 5, subtract 3 from it. Now you have an even number greater than 2. So if you know that every even number greater than 2 is the sum of two primes, you can add 3 (a prime) to it to get your odd number, decomposed into the sum of three primes.
Sadly, it doesn’t work the other way. If you have an odd number written as the sum of 3 primes and subtract one of the odd primes, you’re left with an even number written as the sum of two primes, but there’s no guarantee that all even numbers will show up this way. But the ternary Goldbach conjecture does establish that every even number can be written as the sum of at most 4 primes: just subtract any odd prime number (for example, 3, or 257885161-1 ) from the even number you want to split up, and you’re left with another odd number, which we now know can be written as the sum of three primes. This improves Olivier Ramaré’s 1995 theorem that every even number is the sum of at most 6 primes.
Helfgott’s result is a big deal, but it didn’t come as a lightning bolt from the heavens. His work is part of a long line of papers using a technique called the Hardy-Littlewood-Vinogradov circle method. (Catchy, huh?) The very general idea of the circle method is that we turn a question about a set of numbers, in this case the primes, into a question about integrals over circles using techniques originally coming from analysis in the complex plane. It seems kind of miraculous that it’s even possible to convert questions about integers, which are spaced out discretely on the number line, into questions about continuous functions. “Questions of distribution of primes, or integers, can be expressed naturally in terms of the properties of continuous functions defined in terms of them,” Helfgott wrote in an email. A more concrete explanation of the circle method is beyond me, but if you want to dig into it and its limitations a bit more, you can check out this post by Terence Tao. It’s not for the equation-averse.
via bisrgodel
