power of math 240BC

[dragon]

Damn this guy was good discovering the circumference of the earth beofer anyone else.

240 B.C.: Greek astronomer, geographer, mathematician and librarian Eratosthenes calculates the Earth’s circumference. His data was rough, but he wasn’t far off.

Eratosthenes was an all-around guy, a Renaissance man centuries before the Renaissance. Some contemporaries called him Pentathalos, a champion of multiple skills. The breadth of his knowledge made him a natural for the post of librarian of the library of Alexandria, Egypt, the greatest repository of classical knowledge.

His detractors, however, mocked Eratosthenes as a jack-of-all-trades and master of none. They called him Beta, because he came in second in every category.

Envy? Perhaps. He invented the Sieve of Eratosthenes, an algorithm for finding prime numbers still used in modified form today. He sketched the course of the Nile from the sea to Khartoum, and he correctly predicted that the source of the great, life-giving river would be found in great upland lakes.

Eratosthenes knew that at noon on the day of the summer solstice, the sun was observed to be directly overhead at Syene (modern-day Aswan): You could see it from the bottom of a deep well, and a sundial cast no shadow. Yet, to the north at Alexandria, a sundial cast a shadow even at the solstice midday, because the sun was not directly overhead there. Therefore, the Earth must be round — already conventionally believed by the astronomers of his day.

What’s more, if one assumed the sun to be sufficiently far away to be casting parallel rays at Syene and Alexandria, it would be possible to figure out the Earth’s circumference. Eratosthenes computed the shadow in Alexandria to be 1/50 of a full 360-degree circle. He then estimated the distance between the two locations and multiplied by 50 to derive the circumference.

Of course, his measurements were slightly off. Alexandria was not due north of Syene, but 2 degrees of longitude off. Syene was not precisely on the Tropic of Cancer but 39 minutes of latitude north of it. The distance between the cities was an estimate. The Earth is not a perfect sphere, but an oblate spheroid flattened at the poles.

And we don’t know today the exact size of the measurement unit Eratosthenes was using when he came up with the final figure of 252,000 stades. (We know he knew it was just a rough estimate, because he adjusted his initial number of 250,000 upward by 2,000 — or 0.8 percent — to make it divisible by 60 or 360 for easy computation.)

So how big is 252,000 stades? Depending on which classical source you trust, it’s somewhere between 24,663 and 27,967 miles. The accepted figure for equatorial circumference today is 24,902 miles. Pretty darn good for a guy without modern measurement tools.

Eratosthenes went further and computed the tilt of the Earth’s axis to within a degree. He also deduced the length of the year as 365¼ days. He suggested that calendars should have a leap day every fourth year, an idea taken up two centuries later by Julius Caesar.

Grade-school tales aside, it was thus known long before Columbus that the Earth was round and even how big it is, approximately. But it was just not widely known among the masses in 15th-century Europe. One reason is that Eratosthenes’ very own library of Alexandria had been destroyed, and there was no complete backup of its data

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[fgalkin]

Welcome to middle school?

Have a very nice day.
-fgalkin

[dragon]

Welcome to middle school?

Have a very nice day.
-fgalkin

What are you babbling about? Are you refering to the histroy portion or the math behind it. If you consider the it was wasn't till thousand and more years later that the earth being round was accepted especially which the church resisting it. And while the math it self is basic the idea at his time was not.

Also my coworker wife is a substitute math teacher for middle school and I showed her this and your comment and she laughed that a middle schooler would understand the concepts behind it.
So if you have nothing usefull to say then don't post.

[fgalkin]

How is this a SLAM thread? What is there to discuss? All of this has been known since 240 BC!

And yes, I learned the history part of it in my first year of Geography, sixth grade or so, and the Math portion in 6th or 7th grade. It's just finding an unknown angle in a right triangle, and then calculating the circumference of a circle- basic trigonometry.

I know that the US education system sucks balls- I haven't learned a thing in math or science in one of NYC's top magnet schools that I didn't already know from middle school, and I've always been a retard when it comes to numbers. A friend of mine who actually went to math school took and is good at it, took and passed AP exams out of Russian eighth grade- not because he was a genius (although he is quite smart), but because he has been already taught this.

However, it's the comment that middle school kids are incapable of understanding basic trig is what I find disturbing. WTF? Incapable? What kind of patronizing defeatist bullshit is that? Has she even tried?

Have a very nice day.
-fgalkin

[fgalkin]

Also, the idea that the Earth being spherical was rejected by most is a myth- hell, even Dante refers to a spherical Earth in the Divine Comedy; the orb, representing the world, is a part of numerous royal regalia, etc Sure, some people believed in a disc, rather than a sphere, because people didn't understand gravity, and had a problem with the concept of people living on the antipodes. Sure, there were many theologians who believed in a flat Earth based on the Bible, but the evidence was pretty overwhelming even then that the scientific community had accepted a spherical Earth model.

Have a very nice day.
-fgalkin

[Thanas]

Actually, the orb in most regalia is a direct descendant from the greek Nike/Roman Victoria orb or the Roman Emperor's orb. The significance of those has never been really decided among historians. Some claim it symbolizes the earth, most think it does not symbolize the earth but the philosophical/celestial spheres and a very tiny minority thinks it symbolizes a ball which can roll either way (luck symbol). I myself do not believe in the latest but find the celestial sphere viewpoint most convincing.

[dragon]

Well considering great greeks like Plato and Archimedes whom were unable to determine the circumference of the earth and a person whom was considered a Beta is what we are discussing after all hind sight has it's advantages.

Plato figured the earth was 39 thousand miles while Archimedes was 34 thousand. So sweet look our middle schoolers are smarter than Plato becasue the students can figure it out while the Great Plato couldn't.

So now we can make fun of all the people that attempted to fly before the Wright Brothers and failed because principles of fligh is taught in schools as well.

K now that Scarcasm is out of the way. I wasn't posting this because of the math involved but the fact that someone considered a Beta by his Peers was able to do something they couldn't

Also it goes in SLAM because Math and such is a science after all thats why it says Bachelor of
Science on my Math degree. Fat lot of good that did me.

[fgalkin]

Well considering great greeks like Plato and Archimedes whom were unable to determine the circumference of the earth and a person whom was considered a Beta is what we are discussing after all hind sight has it's advantages.

So? What is your point?

Plato figured the earth was 39 thousand miles while Archimedes was 34 thousand. So sweet look our middle schoolers are smarter than Plato becasue the students can figure it out while the Great Plato couldn't.

Nowhere did I say that middle schoolers are smarter than Plato. They might be smarter than YOU (in fact, I am almost sure of it), but not the greatest minds of antiquity. Just as you're not smarter than Newton just because you've barely passed calculus. I don't understand what the hell is your point?

Also, Plato was not a mathematician,his numbers were a guesstimate. Archimedes didn't travel much outside of Syracuse, so his ability to make observations in various cities was limited, etc. There are many factors why some one makes a discovery, and others don't.

So now we can make fun of all the people that attempted to fly before the Wright Brothers and failed because principles of fligh is taught in schools as well.

I wasn't making fun of Eratosthenos, I was making fun of YOU, because you've apparently just heard of him.

K now that Scarcasm is out of the way. I wasn't posting this because of the math involved but the fact that someone considered a Beta by his Peers was able to do something they couldn't

I think you may be misunderstanding what Beta actually means. Remember, they also called him Pentathalos, the equivalent of "Renaissance Man." He was second best in every category, but he was in EVERY category. It's like being called a second-best physicist after Einstein, second-best painter after Picasso, second-best composer after Stravinsky, second-best boxer after Muhammad Ali, etc.

Second-best does not mean "bad."

Also it goes in SLAM because Math and such is a science after all thats why it says Bachelor of
Science on my Math degree. Fat lot of good that did me.

Are we discussing math? What is there to discuss? If anything, we are discussing history.

Also, the problem with your BS degree is not with the degree- it is with you. My friend from the earlier post had no problem turning his into a Princeton PhD, others used them to get six-figure Wall Street jobs, etc. There are plenty of things to do with a math degree.

Have a very nice day.
-fgalkin

[madd0ct0r]

yeah - this came up in a phis lesson when i was about 14...

[Spoonist]

Me, I liked the reminder though. Lot's of that stuff is 30 years ago so a nudge here and there is always nice.
Sometimes you know the story but not the name, then it's hard to look for it.

Whatever fgalkin is on about, I don't know. It seems like some form of grumpy bragging...

[PeZook]

I never heard of Eratosthenes in middle school, but we did do similar problems in...sixth or seventh grade, I think. Middle schoolers are perfectly capable of understanding trig, at least in such a basic form.

[fgalkin]

Me, I liked the reminder though. Lot's of that stuff is 30 years ago so a nudge here and there is always nice.
Sometimes you know the story but not the name, then it's hard to look for it.

Whatever fgalkin is on about, I don't know. It seems like some form of grumpy bragging...

It was a response to dragon's ludicrous assertion that middle schoolers are incapable of understanding basic trigonometry.

Have a very nice day.
-fgalkin

[Simon_Jester]

Did you HAVE to go looking for bullshit to nitpick over?

[Magis]

Me, I liked the reminder though. Lot's of that stuff is 30 years ago so a nudge here and there is always nice.
Sometimes you know the story but not the name, then it's hard to look for it.

Whatever fgalkin is on about, I don't know. It seems like some form of grumpy bragging...

It was a response to dragon's ludicrous assertion that middle schoolers are incapable of understanding basic trigonometry.

Have a very nice day.
-fgalkin

It seems to me like you were being a prick from your very first post in this thread. That aside, solving the problems mentioned in the OP isn't just a matter of "basic trigonometry" or even just a matter of solving trigonometric equations. Firstly, problem has to be mathematically modelled, with any necessary assumptions, so that it can be identified which equations need to be solved. That is commonly the hardest part of a problem. So, if you were to tell some middle schoolers that at some city at high noon the sun cast a shadow at whatever angle, and at some other city at high noon the sun cast a shadow at some other angle, how many of those students do you seriously expect would formulate the equations correctly? They would probably think about it for a few minutes and then give up and move to the next problem.

And by the way, saying that "finding an unknown angle in a right triangle, and then calculating the circumference of a circle" is the same as understanding basic trigonometry is like saying that knowing i*i=-1 is the same as understanding basic complex analysis. In other words, that's ridiculous, and you're dumb. Have a very nice day.

[madd0ct0r]

yeah - for fun i tried this this morning. Rules: only observation, only a compass and straight edge and mathematical laws I assume the greeks knew.

I got as far as:

case 1 - Suns rays are straight and parrallel, so shadow is caused by earth's curvature
case 2 - Suns rays are straight and from a single point. The shadow is caused by this and the earth is flat
case 3 - Suns rays are straight and from a single point. This AND the earths curvature cause the shadow
case 4 - Suns rays are weakly affected by gravity (have a trajectory over huge distances). This causes the shadow, the earth is flat
case 5 - Suns rays are weakly affected by gravity. This AND the earth's curvature cause the shadow.

From a single data point you can't tell between case 1 and 2, let alone the others.

[Simon_Jester]

Whether middle schoolers could solve this problem depends entirely on the middle schoolers. A typical random sample of middle schoolers would probably not solve the problem, unless you gave them hints and punished them harshly. They might be able to do it then, but realistically you'd just get a bunch of exasperated "this is bullshit" out of them if you weren't careful and hadn't laid the groundwork.

Laying the groundwork takes months.

People who volunteer to use mathematical thinking and reasoning to solve problems even when they don't have to are rare.

[fgalkin]

I am not sure how people went from "The story of Eratosthenes and the math behind it is taught to middle schoolers" to "middle schoolers can do it." Obviously, not every middle schooler will be able to do it, hell not even every adult can, because, as you say, people who apply mathematical thinking and reasoning to solve problems even when they don't have to are rare. On the other hand, someone like this might, but that is beside the point, because I never claimed that the problem could be solved by middle schoolers.

Have a very nice day.
-fgalkin

[Simon_Jester]

Since you started with this random sneer, and things went downhill from there...

Is it any wonder you were misunderstood?

[fgalkin]

Do we have a thread in SLAM every time it's the anniversary of, say Newton's discovery of the Laws of Motion? How is restating something that is common knowledge worthy of a SLAM (as opposed to, say, Testing) thread?

Have a very nice day.
-fgalkin

[D.Turtle]

I think enough has been said on this topic.