How Large is the Great Pyramid of Giza? -- Would it make a wall that would enclose France?
Summary
In this Spreadsheets Across the Curriculum module, students do an estimation calculation that sheds light on the size of the Great Pyramid. The calculation was first done by Napoleon during the Battle of the Pyramids in 1798. While members of his party explored the great structure, Napoleon relaxed at its base and did what is now known as a back-of-the envelope calculation. When his men returned, he announced that there was enough stone in the Pyramid to construct a wall around France. The students build a spreadsheet to recreate this calculation. They find that Napoleon had the magnitude correct.
The module features the writing of the late I.B. Cohen, renowned scholar of the history of science, from his last book The Triumph of Numbers (2005). The module includes links to information about the Pyramid of Giza, the Battle of the Pyramids, Prof. Cohen, and why geologists and geographers know that there are 640 acres in a square mile.
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Learning Goals
- Gain experience in solving a problem approximately by making rough, order-of-magnitude assumptions and then carrying out the calculation.
- Make use of unit conversions involving acres.
- Recall (or be reminded of) the formula for the volume of a pyramid and use it in a calculation.
- Consider how to get length given the volume and cross-sectional area.
- Develop a spreadsheet to carry out a calculation.
- Use the back-of-the-envelope calculation to marvel at one of the Seven Wonders of the World.
- Be introduced to one of the fine, readable books relating to quantitative literacy.
- Begin to see the value of calculations based on approximate assumptions.
- Increase their skill at unit conversions.
- Distinguish conceptually between areas and volumes.
- From the first part of the problem, see an interesting use of a formula from solid geometry.
- From the second part of the problem, take an important conceptual step toward integration (finding a volume by adding up the areas of cross-sectional slices).
- Be impressed with how useful school mathematics can be in appreciating the world outside of a technical context.
Context for Use
I use this module in my Computational Geology course, GLY 4866 (Acrobat (PDF) 39kB Sep25 06). I wrote the moodule for SSAC with the objective that it be of interest outside the geology curriculum (e.g., geography, history).
In the context of Computational Geology, this module provides the students with their first experience in estimation ("back-of-the-envelope problems," "Fermi probelms"). The module comes in the fourth week of the semester, by which time the students have become familiar with spreadsheets and Polya's How to Solve It heuristic. The students work through the module as a homework assignnment after an in-class problem-solving session. I start the session by reading the quotation on Slide 3, visiting the links on Slides 3 and 4, and asking the question on Slide 4. The students then divide into 3- to 4-person groups and work out their answers to the question. Along the way, they torment over the size of an acre, and after a while I review the material in the end note of Slide 14. Students then worry about the size of France. That gives me the opportunity to elaborate on the nature of estimation problems. I do not show them Slide 15. They see that slide during the homework activity in which they build the spreadsheet that does the calculation.
Description and Teaching Materials
If the embedded spreadsheets in the PowerPoint module are not visible, save the file to disk and open it from there.
This PowerPoint file is the student version of the module. An instructor version is available by request. The instructor version includes the completed spreadsheet. Send your request to Len Vacher (vacher@usf.edu) by filling out and submitting the Instructor Module Request Form.
Teaching Notes and Tips
Assessment
The end-of-module questions can be used for assessment.
The instructor version contains a pre-test