Approximation of π *_* Aryabhata worked on the approximation for pi (π) and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes: चतुराधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्राणाम्। अयुतद्वयस्य विष्कम्भस्यासन्नो वृत्तपरिणाहः॥ caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ. 'Add four to 100, multiply by eight, and then add 62,000. By this rule, the circumference of a circle with a diameter of 20,000 can be approached.' *_* This implies that the ratio of the circumference to the diameter is ((4 100) × 8 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures. *_* It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi (π) was proved in Europe only in 1761 by Lambert. - Study24x7
Social learning Network
study24x7

Default error msg

Login

New to Study24x7 ? Join Now
Already have an account? Login
googlePlay app_img
Maths
883 followers study24x7 03 May 2019 07:11 PM study24x7 study24x7

Approximation of π *_* Aryabhata worked on the approximation for pi (π) and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), he writes: चतुराधिकं शतमष्टगुणं द्वाष...

See more

Approximation of π *_* Aryabhata worked on the appro...
IIT Entrance Class 5 Class 6 Class 7 ...
Like | 2 Comment Share
study24x7
Write a comment
Related Questions
500+   more Questions to answer

Popular Courses

Revision batch for Physics (12th cl... All Levels English By V PLUS U
R.S. Aggarwal Solutions Class XII All Levels English By RS Aggarwal FanClub
Class 12 Video Tutorials (English M... All Levels English By CBSE Study Materials
Reasoning Special by Parwez Sir for... All Levels हिन्दी By Reasoning special by Parwez Alam
Advanced Foundation Engineering All Levels English By Kousik Deb
Nutrition, Therapeutics and Health ... All Levels English By Dr. V. Vijaya Lakshmi
Spoken English Beginners Level हिन्दी By Pavitra Language Point for English
Class 11 Video Tutorials (English M... All Levels English By CBSE Study Materials
SSC CGL, CPO, CHSL, GD Comprehensiv... All Levels English By Topline Coaching 3,999 5,499 27% off
NOC:Software Engineering All Levels English By Prof. Rajib Mall
Featured Courses
Popular Pages

Featured Courses

R.S. Aggarwal Solutions Class XII All Levels English By RS Aggarwal FanClub
FREE
4.0
Basic Crop Production Practices (BCPP) All Levels English By Prof. J. R. Yadav Dr. Vinod Kumar Dr. Sharwan Kuma...
FREE
5.0
BESTSELLER
Reasoning Special by Parwez Sir for all Government... All Levels हिन्दी By Reasoning special by Parwez Alam
FREE
5.0
English Special Course for SSC CGL, CPO, GD All Levels English By Topline Coaching 999 5.0
Spoken English Beginners Level हिन्दी By Pavitra Language Point for English
FREE
5.0
Issues in Bioethics (Video) All Levels English By Dr. Sreekumar Nellickappilly
FREE
5.0
Online Free SSC Mock Tests All Levels English By Topline Coaching
FREE
4.5
SAMPLE PAPER CLASS 9 All Levels English By CBSE CLASS 9
FREE
5.0
Dairy and Food process and products technology All Levels English By Prof. Tridib Kumar Goswami
FREE
4.5
Ratio,Proportion and Partnerships for Bank and SSC... All Levels हिन्दी By logicalangle
FREE
5.0

Popular Pages

SAT (Scholastic Assessment Test)

18 followers

Reasoning special by Parwez Alam

148 followers

Study24x7

1218 followers

Henry Harvin

58 followers

RS Aggarwal FanClub

537 followers

SSC Preparation Strategies & Study Mater...

1541 followers

CBSE Study Materials

83 followers

Pavitra Language Point for English

604 followers

Banking/IRDA

265 followers

Guru Dronacharya Academy

63 followers

Get the App

Download the Study24x7 App, so you can connect and collaborate.

study24x7
study24x7
Most Related Articles