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Project 19 : Mathematical Study of Coins

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Rakhee Mishra

 

                    


                Mathematical Study of Coins

Look at the coins that you use every day. Did you know that collecting coins is a hobby called **Numismatics**?

 This fascinating hobby gives us a window into the history of our country and the world. Each coin tells a story – about the era it was minted in, the leaders in power, and the technology available at the time.


https://mycoincollection2023.blogspot.com/2024/05/my-mothers-coin-collection-enduring.html

 

World over , the size, weight, and materials used in coins have changed over the years. Can you guess why?
– Was it to reduce production cost?
– Was it due to the changing value of metals?
– Or because of new minting technologies?

This project invites you to take a deep dive into the world of coins – but with a special focus on **Mathematics**!

Objectives

- To understand the physical and mathematical properties of coins.
- To link real-life objects to mathematical concepts like geometry, measurement, volume, and density.
- To explore the historical and economic significance of coin design changes over time.

Project Sections

1. Historical Overview

- Brief history of coins in India.
- Changes in design, metal, and mint marks.
- Collect and document at least 3 different coins from different decades, preferably of the same value
- Take clear photographs or paste actual rubbings.

If you so wish, you may consider coins of other countries.

Example –

1.      https://mycoincollection2023.blogspot.com/2024/05/a-brief-history-of-modern-australian.html

2.     https://mycoincollection2023.blogspot.com/2024/05/largest-coin-in-my-collection.html

2. Geometrical Study

- Most coins are cylindrical in shape( though not always).
- Measure the following for each coin :

 ( For the purpose of calculations, it would be sensible to use cylindrical coins)

                                        
  * Radius (r): ______ cm
  * Thickness (h): ______ cm


- Use formulas:
  * Area of face: A = πr²
  * Circumference: C = 2πr
  * Volume: V = πr²h

(How would you find the volume of a coin without using the formula?)

3. Density Calculation

- Use a digital scale to weigh the coin (mass in grams).
- Use the formula: Density = Mass / Volume
- Compare the densities of coins from different years.
- What do the results tell you about the metals used?

4. Coin Toss Probability

- Toss a coin 30 times and record heads and tails.
- Calculate the experimental probability.
- Compare with theoretical probability (½).

- You may repeat the experiment with 2 coins or more

Conclusion

Coins are more than currency – they are historical documents and mathematical models. Through this project, you've explored how Math connects with the real world. From geometry to history, and from probability to material science – all from the palm of your hand!



MARKING SCHEME

 

Section

Criteria

Marks

1.      

Historical Overview

Relevance and clarity of historical info; presentation of at least 3 coins

10

2.      

Geometrical Study

Accurate measurements; correct area, volume, and circumference calculations

10

1.      

Density Calculations

Proper weighing, volume computation, and use of density formula

10

2.      

Coin Toss Probability

Clear experiment execution, data recording, and analysis

10

3.      

 Presentation & Conclusion

Neatness, logical flow, and reflection in the conclusion

10

 

Total

50

 










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Location: Ajmer, Rajasthan, India

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