#geometry

mkwadee@diasp.eu

Imagine a circular wheel rolling, without skidding, on a flat, horizontal surface. The #locus of any given point on its #circumference is called a #cycloid. It is a #periodic #curve over a length equivalent to the #circle's circumference and has #cusps whenever the point is in contact with the surface (i.e. the two sides of the curve are tangentially vertical at that point).

Interestingly, it is also the curve that solves the #Brachistochrone problem, which means that starting at a cusp on the inverted curve (maximum height), a frictionless ball will roll under uniform gravity in minimum time from the start to any other point on the curve, even beating the straight line path.

#Mathematics #Geometry #Maths #AppliedMathematics #Mechanics #Kinematics #Dynamics #Physics #MyWork #CCBYSA #WxMaxima

nowisthetime@pod.automat.click

#Geometry of the #Goddess at #GöbekliTepe and #KarahanTepe pt.1 | #HughNewman | #Megalithomania 2022
https://www.youtube.com/watch?v=v5AqNBdrrDQ

Hugh shares new research from southeast Anatolia, looking at the time before Göbekli Tepe, how the site came into being and how geometric principles found in British stone circles are also found here and at Karahan Tepe. Hugh and JJ Ainsworth discovered a Winter Solstice alignment at Karahan Tepe and this is detailed with new research in this lecture. This led JJ to deciphering symbols at this site and others, revealing goddess cults throughout the ‘Tas Tepeler’ region. Part 2 (with JJ) will be available to watch soon.

ramnath@nerdpol.ch

Frank Hoogerbeets, a dutch seismologist who predicted the Turkish quake suggests a convergence of critical #planetary #geometry around 2 and 5 March may result in large to very large seismic activity, possibly even a mega-thrust earthquake around 3-4 March and/or 6-7 March.

Quote He predicted the horror. Now he warns again: The first week of March is critical

#Dutch #seismologist #FrankHoogerbeets said the world could be hit by another major #earthquake in the coming days.

SOURCE: B92, M.J. WEDNESDAY, MARCH 1, 2023 | 15:30

Just to recall that Hoogerbeets gained international fame after predicting devastating earthquakes in #Turkey and #Syria last month.

The first week of March will be "extremely critical", says Frank Hoogerbeets. Hoogerbeets, who makes his forecasts based on the movements of celestial bodies, posted a video on YouTube on Monday warning that "the first week of March will be extremely critical".

"A convergence of critical planetary geometry around 2 and 5 March may result in large to very large seismic activity, possibly even a mega-thrust earthquake around 3-4 March and/or 6-7 March", it is stated in the description of the clip.

In the video itself, the seismologist claimed that the strength of the alleged upcoming earthquake "could be over 8 on the Richter scale."

The affected area could stretch for thousands of kilometers, from the Kamchatka Peninsula and the Kuril Islands in the Russian Far East, all the way to the Philippines and Indonesia, Hoogerbeets said.

"I'm not exaggerating. I'm not trying to create fear. This is a #warning," insists the scientist, who works at the Geometric Survey of the #SolarSystem (SSGEOS).

The head of the Kamchatka branch of Geophysical Research of the Russian Academy of Sciences, Danila Chebrov, questioned Hoogerbeets' predictions and described him as an "amateur".

The connection between the motion of planets in the solar system and seismic activity on Earth "is quite weak, and it is problematic to use it as a main prognostic tool," Chebrov explained.

On February 3, Hoogerbeets posted a tweet that read: "Sooner or later a magnitude 7.5 earthquake will occur in this region (South Central Turkey, #Jordan, Syria, #Lebanon)." Three days later, a magnitude 7.8 earthquake struck Turkey and Syria. The disaster caused the death of more than 50,000 people, and strong aftershocks continue in the region to this day.

Dutsch's seismologist Hoogerbeets has made predictions over the years that have not come true.

Commenting on his work earlier this month, Susan Huff of the US Geological Survey insisted that no scientist "has ever predicted a major earthquake".

Huff told NPR that the direct forecast for the earthquakes in Turkey and Syria was just a coincidence.

"It's a stopped clock that's right twice a day, basically," she said.

Source: https://youtube.com/watch?v=Ntd24t68ex4

https://www.b92.net/eng/news/world.p...&nav_id=115504

rhoutman@pod.orkz.net

Open Numerical Engineering LABoratory(ONELAB), Gmsh, GetDP

  • ONELAB (https://onelab.info) is an abstract interface for sharing information between codes. It is an open-source, lightweight interface to #finite #element #software. It is completely free: the default ONELAB software bundle contains the mesh generator Gmsh, the finite element solver GetDP and the optimization library conveks. Many other codes (free or not) can be easily interfaced as well.
  • Gmsh (https://gmsh.info) is a 3D finite element mesh generator with a built-in CAD engine and post-processor
  • GetDP (https://getdp.info) is a general finite element solver using mixed finite elements

INFO PDF https://onelab.info/slides/onelab.pdf

#opensource #floss #engineering #math #3d #mesh #geometry #magnetism #physics #science #electromagnetism #belgium #gmsh #getdp #onelab #android #iphone #windows #linux #mac

yew@diasp.eu

Roman Dodecahedron: History’s Mystery

It is safe to say that there are secrets to the ancient Roman civilization that even a lifetime of scrutiny will not reveal to us. Yet historians and archaeologists continue their pursuit, discovering ever so often an artifact that is at once perplexing and revealing. One such object is the Roman dodecahedron. The hollow object is a bronze enigma with a decahedral shape of twelve flat pentagonal faces. Its presence in central Europe reveals nothing of its purpose. But there are a few hypotheses that have been floated since its first discovery more than 300 years ago.

The first dodecahedron was discovered in 1739 by a local historian in Aston, Hertfordshire along the English countryside. In his report to the Society of Antiquaries, he described the object as “a piece of mixed metal, or ancient brass, consisting of 12 equal sides.” The strange discovery had all antiquarians in a fix, but there was yet more coming their way. Each subsequently discovered object was different in size and built. Most dodecahedron vary between four and 11 centimeters in size and 35 and 580 grams in weight. Each pentagonal surface contains a hole, but the sizes of these holes almost always vary—within a single dodecahedron as well as among various ones. Each of the five vertices has a globular knob. Tinier than a tennis ball, the object seems more like an interesting dice.

By 2016, 116 pieces of dodecahedra were dug up in today’s Belgium, Croatia, France, Germany, Great-Britain, Hungary, Luxemburg, Netherlands, and Switzerland. The northernmost discovery was made at Hadrian’s Wall in Northern Britain. The southernmost was at Arles in France. A single sample made of silver was found in Geneva. Interestingly, no dodecahedron exists in eastern Roman empire as far as we know. Those found in the western region date back to the second, third and fourth century AD. The randomness of their locations as well as the lack of written context has perplexed historians further.

#Romans #Roman #dodecahedra #geometry #corpus #archaeology

mkwadee@diasp.eu

My wife was looking at the properties of #ellipses such as the one where the sum of the distance of all points on the #ellipse from the two foci are the same and how that relates to the standard equation of an ellipse and so I showed her using my scribbly #handwriting and untidy drawings. Unfortunately, it didn't quite hit home and so I wrote these notes up neatly using #LaTeX, which did do the trick.

To put it up here, I converted the #PostScript pages to #PNG format using #GNU #Gimp and the figure was produced using #Tgif.

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#Mathematics #Geometry #TwoDimensional #PlaneCurve #CartesianCoordinates #CCBYSA