Hello Students, This is the chapter of 9th class the use of coordinates, where now you connect with me. I will discuss about introduction of this chapter because this is one of the most improtant chapter of your 9th class new ncert.
In this chapter, Three most of the important concept of 10th class like as distance formula, section formula, mid points.
Introduction of Grid Lines/ Map/Graph Paper in Ganita Manjari Book
A system of coordinates is a structured framework that enables us to use numbers to describe the exact physical locations of points or objects. The idea of ‘grid-based thinking’ and the geometry required to define the locations of points in space—indeed has deep roots in Bharat. Ganita manjari book mainly based on practical. Beacuse if you want to deeply understand any topic of mathematics first of all you know practical of this topic
Sindhu-Sarasvati Civilisation People Used Grids
The first systematic use of grids occurred thousands of years ago — on a massive urban scale—in the Sindhu-Sarasvati Civilisation, where city streets were constructed with striking precision in North–South and East–West directions at uniform distances of about 10 metres apart. This was a coordinate system in practice: a merchant could find a shop or a warehouse by counting North–South and East–West units of distance from the city centre. Used Graph paper also
Baudhayana First Time Observe
Baudhāyana (c. 800 C.E.), as we have seen, later used East–West and North–South lines for his
deep geometric constructions, developing the Baudhāyana–Pythagoras Theorem and thus laying the foundation of coordinate geometry. Putting coordinates on the Earth’s surface later became important for navigation. Ujjayinī was described in the ancient world—at least as early as the 4th century BCE in the early Siddhāntas—as the point marking the central longitude meridian from which all other locations were measured.
Greek Mathematician Ptolemy Works/ Buildup
The Greek mathematician Ptolemy (c. 150 BCE), building on earlier works including that of Hipparchus, later described the latitudes and longitudes of thousands of locations, including ‘Ozine’ (Ujjayinī). Āryabhaṭa (c. 499 CE) replaced the Greek ‘chords’ with ‘sines’, making it much easier to calculate the coordinates of a star or a city. He mapped the sky using Celestial Coordinates, measuring coordinate distances from the ecliptic (the path of the sun).
Brahmagupta Works
Brahmagupta (c. 628 CE) formalised the notion and use of zero and the negative numbers as algebraic entities; in modern coordinate systems, the ‘origin’ is zero and the ‘negative axes’ represent values less than zero. Without Brahmagupta’s work, the four-quadrant Cartesianplane, as we will study in this chapter, would be impossible.
Brahmagupta’s work was translated into Arabic (as the Sindhind), and the Ujjayinī meridian entered Arabic geography under the name ‘Arin,’ serving as the zero-longitude reference for early Arabic maps which also then made use of negative numbers.
Arab scholar Al-Bīrūnī (c. 1000 CE) travelled to India
The influential Arab scholar Al-Bīrūnī (c. 1000 CE) travelled to India, studied the Siddhāntas, and used Indian trigonometric methods to calculate the coordinates of various cities across Asia. Al-Bīrūnī also later perfected the ‘astrolabe’, a handheld device that allowed sailors to find their coordinates by looking at the stars.
Ömar Khayyām (c. 1100 CE)
Ömar Khayyām (c. 1100 CE), who had become an expert in the Indian decimal system and algebraic formalism, was the first mathematician to solve algebraic problems using geometry by interpreting them in terms of coordinates in the plane.
Work of Fermat (1636 CE), René Descartes (1637 CE)
These concepts eventually reached Europe in the 12th century. The final leap occurred when following the related work of Fermat (1636 CE), René Descartes (1637 CE) formalised the fact that any point in a two-dimensional plane could be defined by simply two numbers—representing the point’s distances from two perpendicular axes.
Points and more complex geometric shapes could then be described precisely using algebra and equations, thus bringing the areas of geometry and algebra even closer together. In Grades 9 and 10, you will have a chance to study this amazing coordinate system which has such a rich history in human thought and endeavour.
You will be able to locate objects with pinpoint accuracy. You will also see how using coordinates enables us to visualise algebraic equations as geometric shapes, and vice versa. We begin our study of coordinates with a story that will help you understand these new terms better.
Conclusion
This is the introduction of orienting yourself: the use of coordinates first chapter class 9th new ncert ganita manjari next all post based on excercise 1.1 and 1.2 of riyans rooms. If you like this post you can share on your social media accounts, Fermat (1636 CE), René Descartes (1637 CE) work on coordinates geometry and rene descartes of father of coordinate geometry.
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