Page 20 - Guidelines for Training/ Orientation of Faculty on IKS
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Guidelines for Training/ Orientation of Faculty on IKS
finding the cube root. Formula for the area of a triangle. Bhāskara I on altitude and area
of a triangle. Numerical examples
Area of a circle, trapezium and other planar figures. Approximate value of π.
Computation of tabular Rsines (geometric and difference equation methods).
Approximate formula for Rsine (as given by Bhāskara I). Problems related to gnomonic
shadow. Bhujā-koṭi-karṇa-nyāya, jyā-śara-nyāya and their applications. Arithmetic
progressions. Finding sum of natural numbers, sum of sums, and so on.
Some algebraic identities. Rule of three. Problems on interest calculation. Ekavarṇa-
samikaraṇa and anekavarṇa-samikaraṇa. The Kuṭṭaka problem (sāgra and niragra-
kuṭṭaka). Illustrative examples.
8. Brāhmasphuṭasiddhānta of Brahmagupta
Introduction. Twenty logistics. Cube root. Rule of Three, Five Seven, etc. Mixtures.
Interest calculations, etc. Progressions: Arithmetic and Geometric. Plane figures.
Triangles, right triangles and quadrilaterals.
Diagonals of a Cyclic quadrilateral. Rational triangles and quadrilaterals. Chords of a
circle. Volumes with uniform and tapering cross-sections. Pyramids and frustum.
Shadow problems.
Mathematical operations with plus, minus and zero. Rules in handling surds (karaṇī)
Operations with unknowns (avyakta-ṣaḍvidha). Equations with single unknowns
(ekavarṇa-samīkaraṇa). Equations with multiple unknowns (anekavarṇa-samīkaraṇa).
Equations with products of unknowns (bhāvita). Brahmagupta on kuṭṭaka. The Second
order indeterminate equation (Vargaprakṛti). Bhāvanā principle and its applications.
9. Bakṣālī Manuscript
The discovery of Bakṣālī Manuscript. Its antiquity and uniqueness. Use of symbols.
Symbol for negative sign (kṣaya). Symbol for denoting unknown quantities (yāvatāvat).
Solution of indeterminate equations. Formula for approximate value of surds. Some
interesting problems involving simultaneous equations.
10. Gaṇitasārasaṅgraha of Mahāvīra
Introduction. Arithmetical operations, operations with zero. Squares, cubes, square roots,
cube roots. Arithmetical and Geometric progressions, Citi (summation). Manipulations
with fractions and solutions of equations. Mixed problems including interest
calculations.
Vallīkāra-kuṭṭākara – linear indeterminate equations. Two and more simultaneous
indeterminate equations. Other indeterminate equations. Vicitra-kuṭṭākara – Truthful
and untruthful statements. Sums of progressions of various types. Variable velocity
problem
Plane figures: Circle, Dīrghavṛtta, Annulus. Ratio of circumference and diameter.
Segment of a circle. Janya operations: rational triangles, quadrilaterals. Excavations:
Uniform and tapering cross-sections, volume of a sphere. Time to fill a cistern. Shadow
problems.
11. Development of Combinatorics
Combinatorics in Āyurveda. Gandhayukti of Varāhamihira Mātrā-vṛttas or moric metres.
Prastāra or enumeration of metres of n-mātrās in the form of an array. Saṅkhyā or the
total number of metrical forms of given number of mātrās. The Virahāṅka sequence (so
called Fibonacci sequence. Naṣṭa and Uddiṣṭa processes for finding the metrical form
given the row-number and vice versa in a prastāra. Mātrā-meru to determine the number
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