The full World Championship match results:
Get rythm (Joaquin Phoenix / Johnny Cash)
Hey get rhythm when you get the blues
C'mon get rhythm when you get the blues
Get a rock and roll feelin' in your bones
Get taps on your toes and get gone
Get rhythm when you get the blues
A little shoeshine boy he never gets lowdown
But he's got the dirtiest job in town
Bendin' low at the people's feet
On a windy corner of a dirty street
Well I asked him while he shined my shoes
How'd he keep from gettin' the blues
He grinned as he raised his little head
He popped his shoeshine rag and then he said
Get rhythm when you get the blues
C'mon get rhythm when you get the blues
Yes a jumpy rhythm makes you feel so fine
It'll shake all your troubles from your worried mind
Get rhythm when you get the blues
Get rhythm when you get the blues
Get rhythm when you get the blues
C'mon get rhythm when you get the blues
Get a rock and roll feelin' in your bones
Get taps on your toes and get gone
Get rhythm when you get the blues
Well I sat and listened to the sunshine boy
I thought I was gonna jump with joy
He slapped on the shoe polish left and right
He took his shoeshine rag and he held it tight
He stopped once to wipe the sweat away
I said you mighty little boy to be a workin' that way
He said I like it with a big wide grin
Kept on a poppin' and he'd say it again
Get rhythm when you get the blues
C'mon get rhythm when you get the blues
It only cost a dime just a nickel a shoe
It does a million dollars worth of good for you
Get rhythm when you get the blues
For the good times (Kris Kristofferson)
Don't look so sad. I know it's over
But life goes on and this world keeps on turning
Let's just be glad we had this time to spend together
There is no need to watch the bridges that we're burning
Lay your head upon my pillow
Hold your warm and tender body close to mine
Hear the whisper of the raindrops
Blow softly against my window
Make believe you love me one more time
For the good times
I'll get along; you'll find another,
And I'll be here if you should find you ever need me.
Don't say a word about tomorrow or forever,
There'll be time enough for sadness when you leave me.
Lay your head upon my pillow
Hold your warm and tender body Close to mine
Hear the whisper of the raindrops
Blow softly against my window
Make believe you love me
One more time
For the good times
STABELVOLLEN MEDIA
Copyright of all music videoes, guest photoes and artworks solely belongs to the artists. Copyright of all other resources : Stabelvollen Media.
MODELING THE EARTH
MENU
MEASURING THE EARTH
"Jorda er rund - som en pizza!” (Mikke Mus i den litterære milepælen Langbein Columbus.)
De fleste mennesker er selvsagt kjent med det faktum at vi lever på en jordklode som er (tilnærmet) kuleformet, og likevel er den umiddelbare erfaringen at (om vi ser bort fra fjell og daler) så er landskapet i et avgrenset, men relativt stort område rundt oss stort sett flatt.
Opp gjennom historien har dette også gitt grunnlag for oppfatninger om at jorda i virkeligheten er flat (som ei pannekake).
Alle har hørt historien om da Christofer Columbus ville seile vestover for å finne sjøveien til India - et land som lå mot øst. Columbus’ lyse idé var at man kunne seile rundt jorda mot vest og dermed slippe å seile rundt Afrikas horn.
Men i folks øyne var det én stor hake ved planen:
Jorda var flat, det mente de fleste på Columbus’ tid. Derfor mente de også at han ikke kunne reise vestover til India, men ville seile over kanten av verden og forsvinne i avgrunnen.
Eks. Et enkelt eksperiment kan overbevise oss om at oppfatningen om ei flat jord ikke holder stikk. (se figuren ovedenfor).
Lim to pinner / fyrstikker et stykke fra hverandre på et papr og lys loddrett ned mot papiret (parallellt med pinnene).
Du kan ikke observere noen skygge sålenge lyset er parallellt med pinnene.
Bøy deretter papiret som vist til høyre og lys igjen loddrett mot papiret, Du kan da observere skygge fra minst en av pinnene.
ERATOSTHENES AND THE SIZE OF THE EARTH
Eratostenes (275 - 194 f. Kr.) gjorde ca. 250 f. Kr. en berømt begrening av Jordas radius, som på mange måter viser hvor langt en var kommet i kunnskap om jordmåling og astronomi.
Eratostenes’ jordmåling er et bindeledd mellom geometriens lover,
geografi og astronomi.
Metoden bygget på fire enkle fakta:
1. Lysstråler fra sola kan regnes å være parallelle, siden avstanden
til sola er så stor i forhold til jordas radius.
2. Ei rett linje skjærer over paralleller under samme vinkel.
3. Senit, iakttager og jordas sentrum ligger på ei rett linje.
4. Ved middagstid står solen i iakttagers meridian.
Eratostenes kjente til at Syene (som heter Aswan i dag) ligger 800 km (nesten rett ) syd for Alexandria. (Se fig. ovenfor)
Han hadde lest at i Syene var det en dyp brønn som solen speilet seg i en bestemt dag i året. Da stod solen altså i senit over Syene. Samme dag dannet solstrålene 7,5 grader med vertikal retning i Alexandria.
Radiene fra Jordas sentrum til henholdsvis Syene og Alexandria dannet derfor en vinkel på 7,5 grader med hverandre.
Buelengden mellom Alexandria og Syene langs meridianen var på 840 km. Nå er 72 / 360 = 1/50, så buelengden mellom Alexandria og Syene er 50-delen av hele jordomkretsen.
Dermed kunne Eratostenes finne jord-omkretsen: 50 * 800 km = 40 000 km.
Siden Eratostenes kjente til formelen for omkretsen av en sirkel, kunne han også finne jord-radius, R, som:
R = O / 2pi = 40 000 km / (2 * 3,14) = 6 369 km.
Dette er forbausende nær den korrekte gjennomsnittsverdien for jordradius på 6 371 km.
Feilen i Eratosthenes beregning var altså på kun 100 % * (6 371 - 6369) / 6371 = 3,1 %.
DELAMBRE AND MECHAIN - DEFINING THE METER
The definition of a meter - a revolutionary idea
During the 17th and 18th century many attempts were made to measure the size of the earth , being either the exact length of a meridian from the North Pole to Equator, the aim being to determine a universallly defined length of a meter.
The most famous attempt is probably the determination of the length of the meridian through Paris during the years 1792 - 1799, among others described in the famous book "The measure of all things" by Ken Adler. (Adler, 2004) The French Science Academy, inspired by the revolusionary ideas of the time after the French Revolution in 1789, wanted to define the meter-length independent of any human property or interests and by measures of the earth itself. After the work of two famouse french geometers ... and ..., who managed to determine the length (with one later discovered minor measuring mistake) of the distance along the meridian from Dunkurque to Barcelona, and thereby wa able to calculate the distance of the whole meridian with acceptable accuracy. After this enormous effort, the lenngth of 1 meter then was defined as 1 / 10 000 000 of the distance between the North Pole and Equator along this meridian! In the following years the metric system was built for different kind of measures much as we know it today, with the determination og the meter length as a foundation.
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STRUVE AND THE GEODETIC ARC
The purpose of the Struve Geodetic arcThe pupose of Struve's measurements was to find accurate measures for the shape and size of the earth. The work continued during the periode 1816 - 1865. It consisted in measuring a great number of angles at a great number of points and calculating positions in 13 measurement pints by astronomical observations towards stars.
The first attempt - Struves Gedodetic Arc
A not so well known attempt to determine such a distance took place from 1816 to 1855, is the Struve Geodetic Arc:
It made the very first accurate measurement of a meridian arc.
The so-called Struve Geodetic Arc is a chain of survey triangulations stretching from the city Hammerfest in Northern Norway to The Black Sea.
through ten countries and over 2820 kilometres.The chain was established and used byt the German-born Russian scientist Friedrich Georg Wilhelm von Struve, aiming to establish the exact size and shape of the earth. At first the chain passed merely through three countries, Norway, Sweeden and the Russian Empire.The arc's first point is located in Tartu Observatory in Estonia, where Struve conducted much of his research.
Struve's meridian arc is the longest continuous series of degree measurements conducted with classical methods. 34 of the original measring-points is today on the World Inheritage list of UNESCO.
This extensive international cooperation was lead by the german atronomer Friedrich Georg Wilhelm Struve. The series itself consisted of 265 main points which formed a chain of 258 triangles (plus 60 auxiliary points) roughly along a chosen meridian plane through the observatory at the University of Dorpat (today Tartu in Estonia). The distances in the grid were determined by the transfer of ten bases that were measured very accurately (down to one millimeter per kilometer) using base rods in the toise (French) and sajen (Russian) units of length.
The degree measuring line stretches from Stara Nekrasivka (near Izmail) on the Black Sea to Fuglenes (near Hammerfest) on the Arctic Ocean, a distance of 2,821.853 kilometers.
The meridian arc today passes through ten countries: Norway, Sweden, Finland, Russia, Estonia, Latvia, Lithuania, Belarus, Moldova and Ukraine.
MENNESKENES STORE BYGGVERK - PYRAMIDENE
2600 BC, that is 4624 years ago (2024) the great Kheops-pyramid was finished at the Giza-pyramid complex in Egypt.
It was then the eldest of the Seven wonders of the Ancient World.
Kheops-pyramiden had the following dimensions:
- Square base with sidelengths 230,3 m
- Height 146,6 m (Current 138,5 m)
- Outer volume på (1/3*230,3*230,3*146,6) kbm = 2 591 795 kbm
that is ca. 2,6 millioner kubikk-meter.
Kheops-pyramiden consisted of
- 2,3 million stone blocks, with the shape of straight prisms, each weighing. 2,6 tonn, with a total ca 6 million tons.
- The stone blocks were held together by mortar.
- The stone blocks mainly consisted of local limestone form the Giza plateau, white limestone from Tura and granite from Aswan.
The Greek mathematician Thales (625 BC - 540 BC), could measure the height of a tree without clibing to the top of it.
He placed a stick beside the tree, and waited until the shadow of the stick had the same length as the stick itself.
The the shadow of the tree would have the same klength as the height of the tree, The rest was an elementary measure task and calculation.
Thales knew that the sun-beams comes in the same direction, they are parallell. . Thales also knew that the two triangles drawn in the fugure below has the same shape.Both of them will have a straight (90 degree) angle. The triangles have similar shape. Today it is also important to use triangles and measure angles when making a map and when navgitaing at sea or in the air.
Many historians also thinks that Thales used this method to decide the height of the pyramis in Egypt. (Drawing to the left and below.)
The width b, of the base of the pyramid coud be measured and so could the length of the oyramis shadow, s..
The the height, H, of the pyramid clould be calculated as
H = s + b/2.
Posisjonsbestemmelse på jordoverflaten
A method to decide the latitude for a random point on the surface of the Northern hemisphere of the is decribed in the figures belwow :
REFERENCES
Johannesen, K (2016) Jordgeometri. Kompendium. Lærerutdanningen Nord Universitet. Kyrre Johannesen. 2016.
Alder, K. (2002) The Measure of All Things.The seven year old odyssey that transformed the world. Abacus. London Ken Alder.2002.
Dolan, G. (2003) On the line. Natinal Maritime Museum. Greenwich, London. Graham Dolan 2003.
Kehlmann, D. (2008) Oppmålingen av verden. Gyldendal. Oslo. Daniel Kehlmann. 2008
Sobel, D. (2005) The true story of a lone Genius Who Solved the Greatest Scientific Problem of His Time. Harper Perennial. Dava Sobel. 2005.