How to calculate the Earth’s circumference with pen and paper

Discovering the size of our planet: An old and simple method reveals the size of the Earth

In the exercise of simplicity and genius, Eratosthenes, Greek mathematician of the third century BC. He devised a way to measure the circumference of the Earth using only a stick and its shadow. Today, we will recreate This historical experience Using the tools we all have at home: pen, paper, and A little help from a friend in another city.

Necessary materials

• Sunny day.
• A vertical stick or rod (such as a meter stick).
• A bucket of sand to keep the stick vertical.
• Large sheet of paper to determine the shade.
• Measuring tape or ruler.
• transporter.
• calculator.
• Internet access or a scale map.
• A friend in another city wants to make the same measurements.

Procedure

to prepare

• Find an open place where The sun is visible at noon.
• Plant the stick vertically in a bucket filled with sand. Make sure it is completely vertical With the help of a plumb line or T-square.

Shadow measurement

• Place the paper on the ground so that… The end touches the base of the stick.
• Mark the end of the shadow on the paper every two minutes. Starts about 10 minutes before noon local It ends when the shadow begins to extend again in the afternoon.

Using just paper, shadows and some calculations, we can reveal the oldest calculations on our planet

Solar angle calculation

• Measure the length of the shadow In the shortest time at noon.
• Use a tape measure to Measure the height of the stick From base to tip.
• Draw a right triangle on the paper With the height of the stick as one side (AB), and the length of the shadow as the other side (BC).
• Use a protractor to measure The angle at the base of the club (BAC angle).

Communicate with your friend

• Send your measurements to your friend in the other city and Ask him to send you his message Made the same way.

Calculate the circumference of the Earth

• Determine the distance North and South Between the two cities using a map or online calculator.
• Uses Formula 360 degrees/central angle To calculate how many sectors of that angle can fit into a complete circle.
• Multiply the distance Between cities With this number we get the circumference of the Earth.

Analysis of the results

Once you do the math Earth’s circumference Using the measurements you’ve made, it’s important to compare your results to them The accepted value is about 40.075 km. This comparison will help you evaluate the accuracy of your home experiment and the effectiveness of the method used.

Evaluate the accuracy of your measurements

• Review the measurements you took for the shade and the height of the stick. It is important to ensure that these measurements are as accurate as possible, Because a small mistake can translate into a big difference in the final result.
• Consider the accuracy of the measuring tools used. For example, A common ruler may not provide the accuracy of a premium tape measure.

Factors that may affect accuracy

• Shadow measurement errors: It can be difficult to determine the exact length of the shadow, especially if the end of the shadow is not sharp. In addition, the angle of the sun changes rapidly at noon, which may change the shadow during the measurement process.
• Stick Height: Make sure the stick is completely vertical. Any deviation from the vertical can cause errors in measuring the length of the shadow.
• Weather conditions: The presence of clouds or light fog can affect the visibility and intensity of the shadow, which may alter the results.

The presence of clouds can not only obscure the sky, but it can also obscure the accuracy of our data, reminding us that even in science, clarity is not always guaranteed.

Think about the method

• Think Eratosthenes’ way And its application in the modern context. Although it is an innovative method, It depends largely on the accuracy of local measurements The precise synchronization between two distant points.
• Think about how to use modern measuring techniques and more precise tools They can improve or validate your results.

At the end of this analysis You will gain a better understanding of the reliability of older technologies Compared to modern tools and the precision we can achieve with simple household tools.

Final thoughts on the Earth’s circumference and other curiosities

This experience is not only offered to you Estimating the Earth’s circumference, But it also connects you to the rich history of science, showing that with simple tools and a little ingenuity, We can unlock the secrets of the universe around us. In this way, Eratosthenes not only proved that the Earth is spherical, but he also proved it to us A legacy of scientific curiosity and exploration Who is still alive today.

If you enjoy solving mathematical puzzles, you may find it great to explore the 10 mathematical problems that science has yet to solve, or even learn how to write mathematical equations online with the best editors available. In addition, you may be interested in finding out more about the number pi, its meaning and some curiosities about it, which will undoubtedly enrich your understanding and appreciation of mathematics.

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