scholarly journals JYOTPATTI

2020 ◽  
pp. 155-159
Author(s):  
Sanjay Madhukarrao Deshpande
Keyword(s):  
Regular Polygon ◽  
Rolle’S Theorem ◽  
General Impression ◽  
Addition And Subtraction

<p>Bhaskaracharya ,(Bhaskar II, 1114- 1185 AD),  was one of the great mathematicians in India. His text “<em>Sindhant Shiromani</em>” (SS) was treated as the base of the further research oriented results by most of all the mathematicians after him.<br> SS contains of two parts:, <em>Goladhyaya and Grahaganit</em>. Jyotpatti is the last chapter in <em>Goladhyaya.  Jyotpatti</em> consists of 25 <em>Shloka</em> (stanzas), all in Sanskrit language. It is a general impression that SS contains <em>Lilavat</em>i and <em>Beejganit</em> also, but that is not so.<br> <em>Jyotpatti</em> deals with trigonometry. This was a milestone in developing geometry in India. <em>Jya</em> means sine and <em>Utapatti</em> means creation.  Hence the name <em>Jyotpatti ( jya + upapatti</em>). <em>Jya and Kojya( or kotijya)</em> stand for the Rsine and Rcosine ratios respectively. The trigonometry developed by Bhaskara II is based on a circle of radius R, and not on a right-angled triangle as taught in the schools.<br> After defining <em>Jya, Kotijya and Utkrama</em> (<em>verse jya) </em>etc, Bhaskara  obtains these ratios for the standards angles of 30,45, 60, 36 and 28,(all in degrees) by inscribing a regular polygon in a circle of radius R. Bhaskara called these angles as <em>Panchajyaka. </em>Not only this, Bhaskara developed   these results for addition and subtraction of two angles. This result was further developed for the similar results, for the multiple angles. Bhaskara compares <em>jya and kotijya</em> with the longitude –latitude of earth and those with lateral threads of a cloth.<br> Contents in Jyotpatti (Only a few mentioned here)<br> (1) R jya 45 =R, and other similar R jya values. (All in degrees)<br> (2)  R jya 36 = 0.5878 approx.<br> (3) Sn = side of a regular polygon of n sides = D sin (π/n), D is the diameter of circle in which polygon is inscribed.<br> (4) Derivation of formulae for sin (θ + ϕ) and cosine (θ + ϕ) called as <em>samas bhavana</em> and <em>antar bhavana</em>.<br> (5) Concept of derivatives, that is, δ(sin θ) = (cos θ) δθ etc. Which is Rolle’s Theorem.<br> Indian mathematicians developed trigonometry in different way than that of western mathematicians. Though <em>Jyotpatti</em> is a small text, it is a landmark in development of ancient and medieval trigonometry.</p>

ABOUT INVARIANCE OF ANGLE NOISE DISTRIBUTION PARAMETERS BY AN ARBITRARY N-POINT GEOMETRIC MODEL TO VIEWING ANGLE

2019 ◽  
pp. 32-35
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Regular Polygon ◽  
Geometric Model ◽  
Sea Surface ◽  
Noise Distribution ◽  
Viewing Angle ◽  
Distributed Objects ◽  
Software Complex ◽  
The Earth ◽  
Distribution Parameters ◽  
Equal Power

In this article we consider a problem of reliable modeling of echo signals and angle noise of distributed objects using twodimensional geometric models with random statistically unrelated signals. The conditions that ensure the invariance of distribution parameters of the angle noise generated by an arbitrary N-point configuration of a two-dimensional geometric model are obtained. In the particular case of a model whose emitters are supplied with signals of equal power, the conditions of invariance are reduced to the location of the model points on the plane in the form of a regular polygon. These results can be used to synthesize mathematical models used for simulating reflections from distributed objects and for developing a hardware-software complex for the simulation of electromagnetic fields reflected from the Earth surface, atmospheric inhomogeneities, the sea surface, etc.

Thinking in Action and Beyond

2018 ◽  
Author(s):  
Terezinha Nunes
Keyword(s):  
Hard Of Hearing ◽  
Inverse Relation ◽  
Teaching Approaches ◽  
Multiplicative Reasoning ◽  
Mathematical Concepts ◽  
Logical Organization ◽  
The World ◽  
Mathematical Problems ◽  
Addition And Subtraction ◽  
Learning By Imitation

Before children learn to use language, they learn about the world in action and by imitation. This learning provides the basis for language acquisition. Learning by imitation and thinking in action continue to be significant throughout life. Mathematical concepts are grounded in children’s schemas of action, which are action patterns that represent a logical organization that can be applied to different objects. This chapter describes some of the conditions that allow deaf or hard-of-hearing (DHH) children to learn by imitation and use schemas of action successfully to solve mathematical problems. Three examples of concepts that can be taught by observation and thinking in action are presented: the inverse relation between addition and subtraction, the concepts necessary for learning to write numbers, and multiplicative reasoning. There is sufficient knowledge for the use of teaching approaches that can prevent DHH children from falling behind before they start school.

scholarly journals Regular polygon solutions of the $N$-body problem

1985 ◽  
Vol 94 (2) ◽  
pp. 301-301 ◽  
Author(s):  
L. M. Perko ◽  
E. L. Walter
Keyword(s):  
Body Problem ◽  
Regular Polygon ◽  
N Body Problem

scholarly journals Manipulative Media Technology for Addition and Subtraction of Integers in Elementary Schools

2021 ◽  
Vol 1823 (1) ◽  
pp. 012096
Author(s):  
Anna Yuliwijayanti ◽  
Santoso ◽  
Achmad Hilal Madjdi
Keyword(s):  
Elementary Schools ◽  
Media Technology ◽  
Addition And Subtraction

scholarly journals Addition and subtraction as a valuation mechanism for valuable buildings

2021 ◽  
Vol 1105 (1) ◽  
pp. 012096
Author(s):  
Basim Hasan Almajdi ◽  
Abbas Na’im Mohsin ◽  
Tabark Hussein Ali
Keyword(s):  
Addition And Subtraction
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