1.2

Minor Versionm

## Introduction

Using a piece of string, we measure the length/perimeter of any oddly shaped track/object, e.g. the length of India's coasts and/or borders.

1. ## Step 1 Precautions

• Be careful when handling scissors, take care to avoid its pointed edges.

2. ## Step 2 Step 1 - Some Concepts      • Distance refers to the actual length of the path traced by an object (in this case between A and B).

• Displacement, on the other hand, is the shortest possible path from A to B. It is usually in the shape of a straight line.

• When we deal with straight paths, often the distance and displacement is the same length, but as the paths get more curved; this changes. It also becomes increasingly impractical to measure such paths with a ruler directly.

• Start by making a mark on one end of the string either with a pen or pencil. This will help us mark the start position accurately.

3. ## Step 3 Step 2 - Measuring a Curved Path      • Now take the end of the string that you marked and place it on the glue-stick. With the string in between a thumb and the glue's surface, drag the thread through the glue-stick. This will make the string sticky and will make it easier to trace the path.

• Start placing the string along the path with the marked end at A.

• As you place the string, keep tracing the string with a pen. The marks should cover both the paper and string. This will help in case the string falls away or moves before the complete trace is finished.

4. ## Step 4 Step 3 - Measuring a Curved Path II      • Continue tracing with the string. Try to follow the path as accurately as possible, this will increase the accuracy of the final measurement.

• Once you have reached point B, make a mark on the string.

• Cut the string at this mark. You now have a length of string that is as long as the path on the paper.

5. ## Step 5 Step 4 - Measuring the String    • Remove the string from the paper and measure it with a ruler.

• Be careful not to stretch the string too much while measuring it.

• Make a note of the length you find. In this case we got 24.8 cm for the example path.

6. ## Step 6 Step 5 - Scale Factor Concepts      • This technique for measuring distances, though simple, is quite powerful. We are now going to estimate the perimeter of India using this technique.

• A map with scale factor is required for this. This scale factor can vary from map to map. It represents a ratio between the length on the map and the actual length of the area represented. For example here our scare factor is 1:16,700,000. This means one centimeter length on the map represents 16,700,000 cm or 167 kilometers.

• Alternatively the map's scale factor could be represented graphically. With the length of the lines under the distance number being the scale factor. To find the scale in this case, just measure the line using a ruler and the number of centimeters you get corresponds to the distance number above the line.

• For example our line length is 1.5 cm. So, in this case 1.5 cm on the map represents 300 kilometers. The line is also split into 3 equal parts. Therefore 0.5 cm length on the map represents an actual length of 100 km.

7. ## Step 7 Step 6 - Measuring the Perimeter of India I      • Start again by making a mark on one end of the string. If you are using a different piece of string, then pull it through the glue-stick again.

• Start on any point along the perimeter and make a small line on the paper to mark the start position.

• Now continue along the perimeter, making marks periodically.

8. ## Step 8 Step 7 - Measuring the Perimeter of India II      • Continue placing the string along the perimeter until you reach the point you stared from.

• Now make a mark on the string where it intersects the initial end.

• Using the final mark as reference cut the remaining string off.

9. ## Step 9 Step 8 - Crunching the Numbers • Remove the string from the map and measure it. The string will be too long to measure all at once, so use the marks made in-between to measure in steps.

• Once you have the total length of the string, multiply it with the scale factor to get the actual length.

• In this example we got a string length of 82.5 cm which when multiplied with 1,67,00,000 gives us 1,37,77,50,000 cm or 13,777.5 kilometers. The actual perimeter of India is 15,106.7 kilometers, which is an error of 8.7%.

• This is an interesting point about error in measurement. No measurement can be made with prefect accuracy. The actual perimeter of India has many complex curves made of yet smaller curves, measuring this in more detail would require more and more precise measurements. Do you think there is a limit to this detail?

10. ## Step 10 Troubleshooting

• The stretching of the string can lead to measurement errors. Be sure not to extend the string too much while placing and measuring the string.

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