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Calculus Final Project Spotlight: Math of the Pilgrimage (Hajj)

A student’s mother is completing the Hajj this year, the pilgrimage that Muslims take to Mecca. This is one of the five pillars of Islam (along with prayer, fasting, charity and testifying that there is only one God). All physically and financially capable Muslims must carry out this pilgrimage at least once in their lifetime. This student based her whole project on the Hajj and calculated many different things about it. Specifically, she calculated:

  1. How long it would take to complete each part of the Hajj (once you get there, there are certain rituals during which the pilgrims walk to various places). She used aerial photographs and official information to measure the distance (around 40 km!) and then used an average person’s walking speed to estimate that each pilgrims walks for around 10 hours during the Hajj.
  2. How many people can be expected to attend the Hajj in the future given data from the past 10 years and assuming exponential growth. She used previous data and the basic exponential growth model to make predictions for the next 30 years.
  3. How large the current area around the Kaaba is (the holiest site of Islam around with the Hajj is based). She used GeoGebra and Google Earth software to measure the area.
  4. And how much the area will have to increase in future years to accommodate the extra pilgrims. Based on her predictions of the increase in the number of pilgrims, she mapped out how big the area around the Kaaba will have to be for the pilgrims to all have the same amount of area. She thought it was cool they they would have to restrict the number of pilgrims, or knock down highways in order to keep the area per person the same.

The math wasn’t perfect and there were some crazy assumptions made, but I absolutely loved this project. It was from someone who had told me in the beginning of the year that math wasn’t her thing, and it was really cool to see her get excited about the project because it applied to something really interesting. All the math was very well motivated and taken from a wide range of things that we did this year. Great stuff!

NEXT YEAR: I could see doing some sort of city planning project involving Google Earth that somehow involves population growth. It would be really cool to look at current rates on population increases in areas and see what that would mean for the physical space. I am so happy that a lot of these final projects have translated into great teaching ideas!