Ladawan:Abu Reyhan Biruni-Earth Circumference.svg

Page contents not supported in other languages.
Gikan sa Bikol Sentral na Wikipedia, an talingkas na ensiklopedya

Orihinal na file ‎(SVG na file, nominal na 1,000 × 900 (na) pixel, pakadakula: 16 KB)

An sagunson na ini naggikan sa Wikimedia Commons asin mapuwedeng gamiton kan ibang mga proyekto. Pinapahiling tabi sa ibaba an deskripsyon na yaon sa sagunsong deskripsyon kan pahina.

Hali sa Wikimedia Commons an file na ito asin pwedeng magamit sa ibang proyekto. Mahihiling sa baba an paglaladawan sa pahina kan paglaladawan kan file kaini duman.

Sumaryo

Pagladawan
English: Biruni (973 - 1048) developed a new method using trigonometric calculations to compute earth's radius and circumference based on the angle between the horizontal line and true horizon from a mountain top with known height. He calculated the height of the mountain by going to two points at sea level with a known distance apart and then measuring the angle between the plain and the top of the mountain for both points.

Biruni's estimate of 6,339.9 km for the Earth radius had an error of 0.0026 and was 16.8 km less than the current value of 6,356.7 km. The idea came to him when he was on top of a tall mountain near Nandana in Pakistan. He measured the dip angle using an astrolabe and he applied to the law of sines formula. He also made use of algebra in his calculation.

  • A = Highest point of mountain
  • B = Lowest point of mountain
  • h = Height of the mountain
  • C = Lowest point of true horizon visible from point A
  • O = Centre of Earth
  • α = Dip angle
  • r = Earth's radius

Solution:
The angle AOC = α.
AO=(r+h) is the hypotenuse in triangle AOC.
r=(r+h)·cos(α)
Then the right side can be simplified to find r.

r=h·cos(α)/(1-cos(α))


Français : Biruni (973-1048) développa une nouvelle méthode utilisant la trigonométrie pour calculer le rayon et la ciconférence de la Terre, basée sur l'angle entre la ligne horizontale et l'horizon réel depuis le sommet d'une montagne de hauteur connue. Il calcula la hauteur de la montagne en se rendant en deux points situés au niveau de la mer dont l'écartement était connu, puis en mesurant l'angle entre la ligne horizontale formée par les deux points au niveau de la mer et le sommet de la montagne, et ceci depuis chacun des deux points.

L'estimation de Biruni de 6 339,9 km pour le rayon de la Terre comportait une erreur de 0,26 %, soit une valeur inférieure de 16,8 km par rapport à la valeur actuelle de 6 356,7 km. L'idée lui était venue alors qu'il se trouvait au sommet d'une haute montagne, près de Nandana en Inde. Il mesura l'angle d'incinaison avec un astrolabe et il appliqua la formule des sinus. Il fit également usage de l'algèbre pour ses calculs.

  • A = point culminant de la montagne
  • B = point le plus bas de la montagne
  • h = hauteur de la montagne
  • C = point le plus bas de l'horizon vrai visible du point A
  • O = Centre de la Terre
  • α = angle d'inclinaison
  • r = rayon de la Terre

Solution :
L'angle AOC = α.
AO=(r+h) est l'hypothénuse du triangle AOC.
r=(r+h)·cos(α)
Puis le côté droit se simplifie pour trouver r.

r=h·cos(α)/(1-cos(α))
Petsa
Pinagkunan Sadiring gibo Using Geogebra and Inkscape
Kagsurat Nevit Dilmen
SVG genesis
InfoField
 
The SVG code is valid.
 
This geometry was created with Inkscape…important.
 
and with GeoGebra.
 
 This geometry uses embedded text that can be easily translated using a text editor.

Paglisensya

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
atribusyon share alike
Nakalisensya an file na ini sa irarom kan lisensyang Creative Commons Attribution-Share Alike 3.0 Unported.
Talingkas mo ining:
  • maihiras – makokopya, maipapanao, asin maipapahiling an gibo
  • i-remix – ma-adapt an gibo
Sa irarom kan mga kondisyon na ini:
  • atribusyon – Dapat mong i-credit, itao an link kan lisensya, at itukdo kun may binago ini. Pwede mo ining gibuhon sa dawa anong rasonableng paagi, pero bako sa paaging ineendorso ka o an paggamit mo kan naglisensya.
  • share alike – Kun ire-remix mo, babaguhon, o madagdag sa materyal, kaipuhan mong ipanao an mga ambag mo sa irarom kan parehas o katulad na lisensya.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts English

creator English

some value

author name string English: Nevit Dilmen
Wikimedia username English: Nevit
URL English: http://commons.wikimedia.org/wiki/User:Nevit

copyright status English

copyrighted English

inception English

2010

media type English

image/svg+xml

checksum English

4dd53114d5cd203e9b0011067229c31d0c5ea202

determination method English: SHA-1 English

data size English

16,607 byte

height English

900 pixel

width English

1,000 pixel

Kasaysayan kan file

Pinduton an sarong petsa/oras para mahiling ng file sa puntong idto.

Petsa/OrasThumbnailSukolParagamitKomento
presente05:25, 2 Mayo 2010Thumbnail para sa bersyon kaitong 05:25, 2 Mayo 20101,000 × 900 (16 KB)NevitCrop
05:21, 2 Mayo 2010Thumbnail para sa bersyon kaitong 05:21, 2 Mayo 20101,390 × 1,220 (16 KB)NevitYellow removed
05:19, 2 Mayo 2010Thumbnail para sa bersyon kaitong 05:19, 2 Mayo 20101,390 × 1,220 (16 KB)NevitImage version
05:18, 2 Mayo 2010Thumbnail para sa bersyon kaitong 05:18, 2 Mayo 2010640 × 480 (22 KB)Nevit{{Information |Description={{en|1=Biruni (973 - 1048) developed a new method using trigonometric calculations to compute earth's circumference based on the angle between the horizontal line and true horizon from a mountain top with known height. He calcu

Ginagamit kan minasunod na pahina an file na ini:

Pankinaban na paggamit sa file

Ginagamit kan mga minasunod na wiki an file na ini:

Hilingon an kadagdagan na pankinaban na paggamit sa file na ini.

Metadatos

Igwa nin dagdag na impormasyon an file na ini, baad hali sa kamera o scanner na ginamit para gibuhon o ma-digitize ini.

Kung an file nabago hali sa orihinal kaining estado, pwedeng dai na syertong tama an magkapirang nakalaaag na detalye sa nabagong file.

Kinua sa "https://bcl.wikipedia.org/wiki/Ladawan:Abu_Reyhan_Biruni-Earth_Circumference.svg"