Thinking
Hounslow, UK

Ancient Egyptians used 256/81 as an approximation for pi,~3.16. Their fraction notation is explained here: en.wikipedia.org/wiki/Egyptian_fraction polymath257 wrote: <quoted text> The Babylonians mainly used the equivalent pi=3, which is where the Biblical sources probably got their approximation from. The Egyptians had one value for the circumference and another for the area of a circle. They didn't realize (as the Babylonians did) the connection between the two. Even fractions were problematic at that stage. The Egyptians had the most developed version of fractions, but even theirs was hard to use. The Babylonians had a base 60 system that didn't actually tell the positional value. An analogy would be writing the same thing for 1.2, 12, 120, and 1200. You see, they didn't have a zero.

Since: Mar 11
Lexington, KY

Indeed that wouldn't be the only thing they stole from the Babylonians. polymath257 wrote: <quoted text> Egyptian fractions were unwieldy and were not used in other places. The Biblical results were probably obtained from the Babylonians.

“Think&Care”
Since: Oct 07
Location hidden

Thinking wrote: Ancient Egyptians used 256/81 as an approximation for pi,~3.16. Their fraction notation is explained here: en.wikipedia.org/wiki/Egyptian_fraction <quoted text> That was their version for area calculations, not for circumference calculations, for which they used a different method. Also, 256/81 is not in the form an Egyptian would have used. Except for 2/3, all of their fractions had a numerator of 1.

“Think&Care”
Since: Oct 07
Location hidden

Thinking wrote: Ancient Egyptians used 256/81 as an approximation for pi,~3.16. Their fraction notation is explained here: en.wikipedia.org/wiki/Egyptian_fraction <quoted text> I'd also add that they did NOT use an actual number for their calculations. Instead, they had a procedure that we *today* interpret as saying that pi=256/81. What the ancient Egyptians did, at least according to the Rhind papyrus (a collection of mathematical exercises from about the second intermediate period), was take the diameter, subtract 1/9 of that diameter, then square the result. That gave them their approximation for the area of a circle. If you compare that to the *actual* formula of A=pi*r^2, then you get the pi=256/81 approximation.

Thinking
Hounslow, UK

L'esprit de l'escalier... did they do better than just using 3? Yes they did. polymath257 wrote: <quoted text> I'd also add that they did NOT use an actual number for their calculations. Instead, they had a procedure that we *today* interpret as saying that pi=256/81. What the ancient Egyptians did, at least according to the Rhind papyrus (a collection of mathematical exercises from about the second intermediate period), was take the diameter, subtract 1/9 of that diameter, then square the result. That gave them their approximation for the area of a circle. If you compare that to the *actual* formula of A=pi*r^2, then you get the pi=256/81 approximation.

“Think&Care”
Since: Oct 07
Location hidden

Thinking wrote: L'esprit de l'escalier... did they do better than just using 3? Yes they did. <quoted text> Granted. The first *theoretical* calculation of pi was by Archimedes around 200BC. He obtained 3+10/71 <pi<3+1/7. The latter is the oftused 22/7 for the approximation.

Thinking
Hounslow, UK

Having forgotten the 96 sided polygon method myself, I found this: www.delphiforfun.org/programs/Math_Topics/Arc... Which led me to wonder whether Archimedes would glory in our having generated pi to 10 trillion figures or whether he'd have hoped for a more definite method other than iteration after 2200 years. polymath257 wrote: <quoted text> Granted. The first *theoretical* calculation of pi was by Archimedes around 200BC. He obtained 3+10/71 <pi<3+1/7. The latter is the oftused 22/7 for the approximation.

“Think&Care”
Since: Oct 07
Location hidden

Thinking wrote: Having forgotten the 96 sided polygon method myself, I found this: www.delphiforfun.org/programs/Math_Topics/Arc... Which led me to wonder whether Archimedes would glory in our having generated pi to 10 trillion figures or whether he'd have hoped for a more definite method other than iteration after 2200 years. <quoted text> Given the pi is transcendental, and probably a normal number (digits essentially random), I'm not convinced a more definite method is possible. I also doubt the continued fraction expansion is 'regular' in any reasonable way.


Thinking
Hounslow, UK

Me neither. I just wonder if Archimedes accepted that. polymath257 wrote: <quoted text> Given the pi is transcendental, and probably a normal number (digits essentially random), I'm not convinced a more definite method is possible. I also doubt the continued fraction expansion is 'regular' in any reasonable way.

“Think&Care”
Since: Oct 07
Location hidden

Thinking wrote: Me neither. I just wonder if Archimedes accepted that. <quoted text> Well, Archimedes would not have known about the irrationality of pi, let alone the fact that it is transcendental (or have even understood what it means to be transcendental). The irrationality of pi wasn't known until the middle of the 18th century AD and the transcendence of pi not until 1882.

Thinking
Hounslow, UK

Agree with the points about 1761 and 1882. He may have suspected something was up though, whatever the reason. Archimedes knew for example that root 3 was proving to be a problem to represent as a fraction. polymath257 wrote: <quoted text> Well, Archimedes would not have known about the irrationality of pi, let alone the fact that it is transcendental (or have even understood what it means to be transcendental). The irrationality of pi wasn't known until the middle of the 18th century AD and the transcendence of pi not until 1882.

“It's just a box of rain...”
Since: May 07
Knoxville, TN

polymath257 wrote: <quoted text> Egyptian fractions were unwieldy and were not used in other places. The Biblical results were probably obtained from the Babylonians. I don't think there was any calculation involved. They were describing the pool, not analyzing it. As such, they wouldn't have taken one measurement and then calculated the other, but would have measured them both. The inaccuracy simply shows how crude those measurements were. I've never taken a very close look at the history of mathmaybe it's time to do that. Somehow, I doubt that the early Hebrews will play much of a role in it, though.

Thinking
Hounslow, UK

Judged:
1
Maybe that's why their walls kept falling down... NightSerf wrote: <quoted text> I don't think there was any calculation involved. They were describing the pool, not analyzing it. As such, they wouldn't have taken one measurement and then calculated the other, but would have measured them both. The inaccuracy simply shows how crude those measurements were. I've never taken a very close look at the history of mathmaybe it's time to do that. Somehow, I doubt that the early Hebrews will play much of a role in it, though.

Since: Apr 12
Location hidden

polymath257 wrote: <quoted text>Why would you think that is the problem in the Bible? The number pi was not singled out as a number of independent interest for a few hundred years; the goal was to find the circumference given the diameter. Given that as the problem, if the 10 is a rounded value, then the rounded value of the circumference could be anywhere from 30 to 33. In today's math yes. If you don't have fractions or decimal points and use elbow to finger tip as a ruler then 30 cubits would be accurate because Pi could and would only be "3".

Since: Mar 11
Lexington, KY

Archimedes was an interesting dude light years ahead of his time. Facinating genius. polymath257 wrote: <quoted text> Well, Archimedes would not have known about the irrationality of pi, let alone the fact that it is transcendental (or have even understood what it means to be transcendental). The irrationality of pi wasn't known until the middle of the 18th century AD and the transcendence of pi not until 1882.

Since: Mar 11
Lexington, KY

The ancient Egyptians were an interesting lot. Check out Dr. Kara Cooney a cutie MD on the subject of ancient Egyptians. http://www.youtube.com/watch... Smart and cute! NightSerf wrote: <quoted text> I don't think there was any calculation involved. They were describing the pool, not analyzing it. As such, they wouldn't have taken one measurement and then calculated the other, but would have measured them both. The inaccuracy simply shows how crude those measurements were. I've never taken a very close look at the history of mathmaybe it's time to do that. Somehow, I doubt that the early Hebrews will play much of a role in it, though.

Since: Apr 12
Location hidden

Givemeliberty wrote: <quoted text> http://en.m.wikipedia.org/wiki/Egyptian_fract... Indeed you are correct! No need for people of that time to round up or down or only use while numbers. The ancient Egyptians amongst other cultures were using fractions long before the genesis myth was written. Givemeliberty wrote: I am especially proud of my volunteer work and donations to the humanist cause. Every year I go to the Philippines and spend thousands on food,water, clothing and medicine for the needy there. After a horrific typhoon and flooding there I was there amongst others 14 hours a day handing out supplies, giving life saving injections and treatments to those who lost their home. I stood and watched as homeless children lined up easily 3 miles deep for a package of crackers sandwich fruit and bottle of water. Unwanted children who were born because the Christian ran theocracy light government makes it nearly impossible for a woman to obtain birth control. My wife is in premed classes and wants to practice medicine there free to help those poor children. Here in the states I collect donations for running in marathons with the money going to children's charities and cancer or HIV awareness programs. I have seen first hand time and time again the damage and heart breaking situations brought on by theists. The same theists who come crawling to us to help fix their mess! Oh but while we are fixing it are we thanked? Nope. We barely get the figurative broom in hand and they are shrieking at us for not believing in their imaginary friend. Honor? I guess it is a relative term. The dozen of urban low income students I assist for free with their biology and pharmaceutical homework at two different colleges locally would probably say good ole KJ is an alright dude. Now if coming on topix and giving the theists a little taste of backbone, the theists who try to intimidate and silence non believers because they think we should all be meek and humble and tolerate their abuse and repeated logical fallacies makes me vile, Without reason, Disrespectful, In someone's opinion? So be it, hmmm I will chuckle about how vile And disrespectful I am Friday at U of L for the 6 hours I am assisting the students there as a volunteer. Or perhaps this summer as I am passing out thousands of dollars worth of free medicine and other essentials trying to save some more homeless from dying. Yes I was walking by a group of people there and they were huddled together praying loudly and crying. I looked in and a young girl was on the ground dying of dehydration. Instead of getting her water and rushing her to the hospital they stood there holding hands and praying! I grabbed my cell phone and called for an ambulance and started trying to get her to drink. Slowly she sipped the water as the praying continued. The ambulance came after almost an hour and reluctantly took her to the hospital, the paramedic said she was good as dead and best leave it in the hands of Jesus same thing the crowd thought. She died 18 hours later. They didn't even know her name and couldn't figure it out. I guess I'll somehow deal with being called disrespectful. <quoted text> "I semiretired except for collecting and inspecting my rental properties. I live comfortably off my stock dividends, porn sites I own, early retirement from work and rental properties here in the states and in the Philippines. " OMG. It's getting better all the time!!! You're retired except for Porn and your wife is still in school! You give Christians thousands of dollars of your own money!!!! Baaaaahaaaaaahaaaaa Please stop!!!! Lol BAAAAAHAAAAHAAAAA !!!! Liberty wrote: I am a 32 year old multiracial man with a Johnson bigger than anyone in your family.

Since: Apr 12
Location hidden

Thinking wrote: <quoted text>Civilisations were using fractional approximations to pi long before your POS bible was invented.
Your bible was already out of date when the goatfuckers wrote it. Blood presser check time! LOL

Since: Mar 11
Lexington, KY

Blood what? Presser? Keep scampering into stupidity. Langoliers wrote: <quoted text> Blood presser check time! LOL

Thinking
Hounslow, UK

Oh dear. You're a sandwich short of a full picnic, aren't you, poppet? Langoliers wrote: <quoted text> Blood presser check time! LOL

