Rhind papyrus problem 41 (pi)

[dan.rowling]

Okay, i got a little problem. I have to do a research for school about the history of pi. Not that hard you'd think... But then i found that the Egyptians found 3,1605 for pi in 1650 BC. So now i got to find out how he found it out.
he used the formula: Volume of a cylinder = ((1-1/9)d)²h if you calculate it you get 256/81 r² h so he found 256/81 for pi. But i don't get the start. where did that (1-1/9)d came from? i know it replaces pi r².
I thought it came from the relation between a square and circle, but after looking into that for the last 2 days, i still haven't figured it out.
If someone could help me with this i'd be very grateful.
with regards, dan.rowling.

 

[JeffM]

Okay, i got a little problem. I have to do a research for school about the history of pi. Not that hard you'd think... But then i found that the Egyptians found 3,1605 for pi in 1650 BC. So now i got to find out how he found it out.
he used the formula: Volume of a cylinder = ((1-1/9)d)²h if you calculate it you get 256/81 r² h so he found 256/81 for pi. But i don't get the start. where did that (1-1/9)d came from? i know it replaces pi r².
I thought it came from the relation between a square and circle, but after looking into that for the last 2 days, i still haven't figured it out.
If someone could help me with this i'd be very grateful.
with regards, dan.rowling.

Find Journey Through Genius in a library. One of its themes is the calculation of pi. It is designed to be accessible to high school students, and if I remember correctly, it starts with the Rhind papyrus.

You must be very careful with Egyptology. I suspect that any day now someone will claim that the Temple at Karnak solved some deep problem in string theory.

As nearly as anyone can tell, the Egyptians and the Mesopotamians probably even earlier devised mathematical procedures and approximations that were effective at solving the practical problems that arose from utilizing their technology. It was the Greeks, however, who appear to have begun systematic mathematics.

 

[dan.rowling]

Thank you for your answer, i found the book and started reading it from the point where it's about the rhind.

Edit: unfortunately i can't find the answer in the part about the rhind, so if anyone can please let me know, i searched in Journey Through Genius every part that had something to do with pi according to the index.

 

[JeffM]

Thank you for your answer, i found the book and started reading it from the point where it's about the rhind.

Edit: unfortunately i can't find the answer in the part about the rhind, so if anyone can please let me know, i searched in Journey Through Genius every part that had something to do with pi according to the index.

The answer to what? By the way. Editing a post to continue a question is not a good idea. No one may reread your post to see that it has been edited. If you are asking about quadrature, JTG does explain about quadrature and the Greek interest in quadrature.

 

[dan.rowling]

The big answer that i'm looking for is how that the formula V=((1-1/9)d)²h was set up. And on which this was based. And i thought that this was based on some sort of relation between a circle and a square. But the problem is that they hadn't discovered pi, so i can't use it to proof anything..

 

[JeffM]

The big answer that i'm looking for is how that the formula V=((1-1/9)d)²h was set up. And on which this was based. And i thought that this was based on some sort of relation between a circle and a square. But the problem is that they hadn't discovered pi, so i can't use it to proof anything..

What we know about mathematics before the Greeks is very little. A lot of pre-Greek mathematics may just have been formulas discovered by trial and error, written down, and used when necessary. So when someone says that the rhind papyrus calculated pi, that is a guess. What they mean is that there is at least one formula in it that can be used to calculate an approximation to pi. That does not show that it was used to do that because it does not show that the Egyptians even had the concept of what is now called pi. What is known is that the Greeks were interested in decomposing areas for various shapes and equating them to the area of squares, a process called quadrature. It is still how we measure area, square feet, square kilometers etc. I believe it was Euclid (or one of his immediate predecessors) who identified the concept that is now called pi, and Archimedes who first developed reasoned approaches to calculating approximations. The subject of quadrature, the identification of the concept that we (not the Greeks) call pi, the (unattainable) goal of "squaring the circle," and the first attempts at estimating approximations to pi are topics covered in the book I mentioned (and many other books).

You cannot use a book like JTG as an encyclopedia. It is a mixture of history and math (aimed at high school students so the math is not too hard). It is linear: he starts with the Egyptians and ends with Cantor. He has themes that run throughout the book. If you start in the middle and jump around, you may never see what you are looking for even if it is there. If this book does have the answers to specific questions you have, it may be anywhere in the chapters before Heron and Cardano. Nor may the particular book I mentioned answer any specific question you may have. But it will have a bibliography that will tell you about other books on the same general topics. That is why what you are working on is called a research topic.

 

[DrPhil]

The big answer that i'm looking for is how that the formula V=((1-1/9)d)²h was set up. And on which this was based. And i thought that this was based on some sort of relation between a circle and a square. But the problem is that they hadn't discovered pi, so i can't use it to proof anything..

Was it a measurement? If they deduced that the volume was proportional to d^2 and to h, then comparing the volume (perhaps of sand) of the cylinder to the volume of a square container would give pi empirically.

 

[dan.rowling]

What we know about mathematics before the Greeks is very little. A lot of pre-Greek mathematics may just have been formulas discovered by trial and error, written down, and used when necessary. So when someone says that the rhind papyrus calculated pi, that is a guess. What they mean is that there is at least one formula in it that can be used to calculate an approximation to pi. That does not show that it was used to do that because it does not show that the Egyptians even had the concept of what is now called pi. What is known is that the Greeks were interested in decomposing areas for various shapes and equating them to the area of squares, a process called quadrature. It is still how we measure area, square feet, square kilometers etc. I believe it was Euclid (or one of his immediate predecessors) who identified the concept that is now called pi, and Archimedes who first developed reasoned approaches to calculating approximations. The subject of quadrature, the identification of the concept that we (not the Greeks) call pi, the (unattainable) goal of "squaring the circle," and the first attempts at estimating approximations to pi are topics covered in the book I mentioned (and many other books).

You cannot use a book like JTG as an encyclopedia. It is a mixture of history and math (aimed at high school students so the math is not too hard). It is linear: he starts with the Egyptians and ends with Cantor. He has themes that run throughout the book. If you start in the middle and jump around, you may never see what you are looking for even if it is there. If this book does have the answers to specific questions you have, it may be anywhere in the chapters before Heron and Cardano. Nor may the particular book I mentioned answer any specific question you may have. But it will have a bibliography that will tell you about other books on the same general topics. That is why what you are working on is called a research topic.

Thanks for your answer it helps me a lot. I've found JTG very useful and i can use it for other stuff in my research as well, such a great book. I'll be reading it from start to finish then, but i've found already some stuff in it.

 

[JeffM]

Thanks for your answer it helps me a lot. I've found JTG very useful and i can use it for other stuff in my research as well, such a great book. I'll be reading it from start to finish then, but i've found already some stuff in it.

You're welcome. Good luck on your project and have fun with the book.