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prashant singh
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I want to know how mathematician got the idea of external division , how they can say that a point can divide a line externally, what's the reason behind this discovery . Why they discovered it.
I assume because of the invariance of the ratios under affine mappings, e.g. parallel projections. These mappings are essential to the constructions @jedishrfu mentioned.prashant singh said:Why they discovered it.
The Section Formula is a mathematical formula used to divide a line segment into a given ratio. It is also known as the internal division formula as it divides the line segment internally.
To find the coordinates of a point when dividing a line segment using the external ratio, you can use the following formula:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
Where m and n are the given ratios and x1, x2, y1, and y2 are the coordinates of the endpoints of the line segment.
The main difference between internal and external ratios in the Section Formula is the direction in which the line segment is divided. Internal division divides the line segment internally, while external division divides the line segment externally.
Yes, the Section Formula can be used to divide a line segment into any number of parts. You will need to divide the given ratio by the number of parts + 1 to find the ratios for each division point.
The Section Formula has various applications in fields such as architecture, engineering, and surveying. It is used to divide land or buildings into specific ratios, to design structures with specific proportions, and to determine the center of mass of an object.