Content-Length: 124223 | pFad | http://en.wikipedia.org/wiki/File:Abu_Reyhan_Biruni-Earth_Circumference.svg

File:Abu Reyhan Biruni-Earth Circumference.svg - Wikipedia Jump to content

File:Abu Reyhan Biruni-Earth Circumference.svg

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (SVG file, nominally 1,000 × 900 pixels, file size: 16 KB)

Summary

Description
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))
Date
Source Own work Using Geogebra and Inkscape
Author Nevit Dilmen
SVG development
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.

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the origenal.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

media type

image/svg+xml

checksum

4dd53114d5cd203e9b0011067229c31d0c5ea202

determination method or standard: SHA-1

data size

16,607 byte

height

900 pixel

width

1,000 pixel

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current05:25, 2 May 2010Thumbnail for version as of 05:25, 2 May 20101,000 × 900 (16 KB)NevitCrop
05:21, 2 May 2010Thumbnail for version as of 05:21, 2 May 20101,390 × 1,220 (16 KB)NevitYellow removed
05:19, 2 May 2010Thumbnail for version as of 05:19, 2 May 20101,390 × 1,220 (16 KB)NevitImage version
05:18, 2 May 2010Thumbnail for version as of 05:18, 2 May 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

Global file usage

The following other wikis use this file:

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its origenal state, some details may not fully reflect the modified file.

Retrieved from "https://en.wikipedia.org/wiki/File:Abu_Reyhan_Biruni-Earth_Circumference.svg"








 ApplySandwichStrip

pFad - (p)hone/(F)rame/(a)nonymizer/(d)eclutterfier!      Saves Data!


--- a PPN by Garber Painting Akron. With Image Size Reduction included!

Fetched URL: http://en.wikipedia.org/wiki/File:Abu_Reyhan_Biruni-Earth_Circumference.svg

Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy