Sunday, 11 September 2016

To build mathematical model to compute distance between two places, and compare the result obtained with that from use of technology

At least three specific routes are to be used and distance measured. First the route is selected using Google maps, and copied to GeoGebra to get the coordinates of the path. The scale is measured using Google maps and the derived route (curve) from GeoGebra is used to calculate the length using Regression/Curve fitting etc. The result thus achieved is compared with the distance given by Google Maps. Same method is applied to three specific routes. Each step of Mathematical model needs to be defined in detail. Only given specific (three) routes are to be used. To find a road on Google Maps. An example would be the route from Vikas Kunj, Vikas Puri, New Delhi, India to The British School, Chanakya Puri, New Delhi, India. After choosing the route, the picture is captured and transferred onto a graphing software called"GeoGebra". Thereafter, we need to find a scale for the image in order to be able to calculate the distance accurately. This would require use of a known distance and can be computed through Google Maps. The actual value to the distance on the graph is then compared and scale achieved. After that, plot the points on the road. The coordinates of each point will be automatically presented through GeoGebra. Next, through the process of interpolation, curve fitting or any other method, we need to find the equation of the best fit line for the given coordinates. After this, we need to find out the length of said graph. This would require some usage of Calculus and geometry. Finally, the calculated distance is to be compared with the distance actually provided by the Google Maps and compute % error in our result. This process is to be repeated for three specific routes and results achieved through Google Maps and our Mathematical Model needs to be compared and presented in tabular form. The screen shots from Google Maps, GeoGebra and the drawn graph are to be included in the paper with detailed steps of Mathematical model explained.

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