Just a simple demonstration here of the #locus of #StraightLine in ##ThreeDimensionalSpace in #CartesianCoordinateds passing through a known point with #PositionVector a and a direction d. A #Projection onto the x-y plane is also depicted.
#AnimatedGif #FreeSoftware #WxMaxima #Mathematics #Maths #Geometry #MyWork #CCBYSA
There are literally hundreds of #proofs of #Pythagorus' #Theorem and this book has about three hundred of them. It was published in the 1920s but my copy was printed to order and bound in #India. I hope it will be both a reference and a talking point.
#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.
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.
Making it work
https://img-9gag-fun.9cache.com/photo/aRE0jdj_460svav1.mp4
31 sec video
#video #geometry
#Geometry, #Implosion and the #Alchemy of #Time
Premiered Oct 10, 2022
After a quarter of a century, #JayWeidner and #DanWinter come together to discuss #plasma #physics, #sacred geometry and alchemy. A one time super discussion that you do not want to miss.
#opensource #floss #engineering #math #3d #mesh #geometry #magnetism #physics #science #electromagnetism #belgium #gmsh #getdp #onelab #android #iphone #windows #linux #mac
https://www.youtube.com/watch?v=WFCzAW2nQbQ
#Bosnian #Pyramids – 3 Biggest Discoveries in 2020! -
16 Feb 2021 ... While the World came to the halt, Bosnian #Pyramid project has produced #amazing results in #archaeology, archaeo-#astronomy and #sacred #geometry .
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.
https://www.bitchute.com/video/bNlblwFSroQq/
#RC
#Randall Reveals Ep002 #Astronomy, Geodesy, #Great #Pyramid, #Stonehenge - #Sacred #Geometry & #Coincidence #108
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.
#Mathematics #Geometry #TwoDimensional #PlaneCurve #CartesianCoordinates #CCBYSA
Like last time, you can find a proper translation to english in the comment section below.
Die Mathematiker haben ja keine Hemmungen, mehr als 4 Dimensionen sind überhaupt kein Problem! Ist ja nicht Physik hier, wo die armen Teufel nachweisen müssen, daß die dann wirklich und total echt voll real existieren. Nicht nur so als Freiheitsgrade wie etwa Position und Geschwindigkeit zusammengenommen, was ja bei einem Partikel schon einen 3+3=6 Dimensionen oder Freiheitsgrade ergäbe. Sowas heißt dann Phasen- oder Hilbertraum, und ist Thema der symplektischen Geometrie, einer Abart der Standardgeometrie, bei der das Skalarprodukt auf die Seite gelegt wird, sodaß es null wird wenn die beiden Vektoren parallel sind. Damit kann man z.B. Kepler's elliptische 2d Planetenbahnen in 4d sehen, und die Ellipse ist darin einfach ein Kreis!
Man kann eine Menge zu 4d sagen. Zwei 4d Objekte hatte ich ja schon vorgestellt. Die 3-Sphäre als Oberfläche eines 4-Balls. Und den projektiven PR^3, der einer halben 3-Sphäre ("Hemiball") entspricht, bei der gegenüberliegende Seiten zusammengenäht werden. Weil das schwierig zu sehen ist, hatte ich stattdessen von PR^2 gesprochen, einer Kreisscheibe bei der gegenüberliegende Punkte ihres Randes zusammengenäht werden. Versucht man sowas zu häkeln, dann stellt sich raus, daß das in 3d nicht ohne Selbstüberschneidungen geht. Hätten wir eine extra 4. Dimension, dann wäre das überschneidungsfrei drin. Jakob Steiner fand 1838 während seines Besuchs in Rom eine (beinahe) Einbettung in 3d, such mal nach Steiner'sche Fläche oder "roman surface" für ein Bild. Zugegeben auch nicht ganz einfach zu sehen. Werner Boy fand eine andere Einbettung, "Boy's surface", vielleicht hilft das. Die englische Wikipedia ist recht gut bei sowas.
Für 3-Orientierungen sind die zwei Freiheitsgrade, die man hat wenn man einen Ball auf dem Boden rollt, miteinander verbunden. Das ist nicht so wie wenn man die zwei Richtungen eines ebenen Koordinatensystems addiert. Die Bedeutung der einen Richung ändert sich (auf der Kugel), wenn man die andere entlangrollt. Und wenn man die Kugel in einem kleinen Kreis rollt, dann scheint sie sich um eine dritte zu drehen. Dieser Effekt wird Holonomie genannt. Man kann also unter verwendung von 2 Freiheitsgraden in 3 Richtungen gehen! Zur erinnerung, die 3-Orientierungen bilden einen 3d Raum: Dreh den Nordpol irgendwohin (2 Freiheitsgrade), und kann dann noch eine Drehung entlang der Nordpolachse (noch 1 Freiheitsgrad).
Einen Schritt weiter: Orientierungen eines 4-Vektors bilden einen 6d Raum! Ihr erinnert euch, in 3d war das "zufällig" auch ein 3d Raum. Ich will da diesesmal nicht allzu weit reinsteigen, das oben sollte ja erstmal genug zum nachdenken geben, daher nur ein weiteres Detail: Man kann sich den 4-Spinraum frei in zwei Hälften zerlegen, und jede davon unabhängig von der anderen wie einen 3-Ball drehen!
Es gibt so viel zu sehen. Das hier ist ja nur ein winziger Teil der mathematischen Landschaft. Selbst von dem Kontinent Geometrie haben wir gerade mal eine kleine Promenade am Fuße der Alpen gemacht. Bis nach ganz oben komme ich selber auch nicht (da braucht man eine Spezialausrüstung und ein modifiziertes Gehirn für), und den Ausblick von dort kann ich mir auch nicht annähernd vorstellen, aber ich finde die Landschaft hier unten auch hinreißend. Man darf sich nur nicht an den erfahrenen Alpinisten stören, die scheinbar mühelos senkrecht die Wand hochgehen, wärend unsereins unter vollem Krafteinsatz millimeterweise eine leichte Steigung überwindet.
