Most interesting -- thanks for posting. However, if they were so mathematically advanced; did the Babylonians have a symbol for the concept of zero?

quote:

Originally posted by pillboxesghost:
Most interesting -- thanks for posting. However, if they were so mathematically advanced; did the Babylonians have a symbol for the concept of zero?

Sort of. They had a concept of "nothingness" which they represented as a blank. Later they had a symbol there that they used as a place holder. But from what I read, they did not consider it to be a number.

Again from what I read, They did have decimals or 60inals, or what ever.

Also the whole "better and more accurate than what we have is a bit silly. What they are talking about is that fractions of non-factors of 10 are recurring decimal. For example 1/3 is 0.33333333 forever. But 1/2 is 0.5 exactly. 60 has more factors than 10 so 1/3 can be written as a non-recurring 60inal. However 1/7 can not because 60 is not a multiple of 7. If you choose 13 as a base, all fractions other than 1/13 are recurring 13inals.

This has been an argument for switching to base 12 as it has twice as many factors as 10 but you lose 5 as a factor. Following the French Revolution, they actually considered switching to base 12, but were dissuaded.

You can count to 144 (156 actually) on two hands. You have 12 phalanges in your four non-thumb fingers. Use the tip of your thumb as a place holder. To go past 12, go to the first phalanges on the opposite hand and then restart counting on the first.

Regarding the invention of a better trigonometry. Maybe. Or maybe not. The Babylonians were apparently fascinated by squares and square roots. It may have been a list of square triplets where a^2 + b^2 = c^2. There are also apparently a few miscalculations on it.

Fascinating. But more accurate or a whole new form of math? Not really.

This message has been edited. Last edited by: Fenris,

I also question the idea that Babylonian trigonometry was "more accurate" than what we are taught. The ratios between the sides of right triangles are fixed for a given angle (however expressed) and those ratios can be calculated to whatever degree of precision one needs, in whatever number base. When I worked for a surveying firm, we had trig tables to 12 decimal places and I know that there existed one to 20 decimal places. There are very few practical problems that cannot be solved with tables of that size. Admittedly, the number of digits required for a given precision when using the sexagesimal (base 60) system is fewer, but arithmetic is clumsier. (I don't even want to think about it.)

I'm willing to concede that perhaps the Babylonians (and maybe the Sumerians before them) were able to compute using trigonometry, but I won't agree that their way was necessarily more accurate.

flashguy

This message has been edited. Last edited by: flashguy,

Yes, but could their tablets play Angry Birds?

quote:

Originally posted by flashguy:
Learning to count in base 60 would be a chore.

To say nothing of the times-tables!

quote:

Originally posted by flashguy:
I also question the idea that Babylonian trigonometry was "more accurate" than what we are taught. The ratios between the sides of right triangles are fixed for a given angle (however expressed) and those ratios can be calculated to whatever degree of precision one needs, in whatever number base. When I worked for a surveying firm, we had trig tables to 12 decimal places and I know that there existed one to 20 decimal places. There are very few practical problems that cannot be solved with tables of that size. Admittedly, the number of digits required for a given precision when using the sexagesimal (base 60) system is fewer, but arithmetic is clumsier. (I don't even want to think about it.)

I'm willing to concede that perhaps the Babylonians (and maybe the Sumerians before them) were able to compute using trigonometry, but I won't agree that their way was necessarily more accurate.

flashguy

Reverse Babylonian Notation maybe?

quote:

Originally posted by c1steve:
That is very interesting. Using a Base 60 system, they would have little or no need for decimal places. They must of done much of their math in their heads, and gotten very good at it, as writing supplies were nearly non existent.

They had clay tablets and stylus.

Will this be on the test?

This is great reading, thanks for posting this up, I had no idea.

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Originally posted by SgtGold:

quote:

Originally posted by tacfoley:

quote:

Originally posted by sigfreund:
Interesting article. I’ve often wondered what our arithmetic and mathematics would have been like if we’d had 12 fingers rather than 10.

Hmmmm. I've only got eight fingers. The two lumpier ones on the outside are my thumbs.

I agree, however, that we have ten digits.

tac

All thumbs are fingers, but not all fingers are thumbs.

You've never seen me try to jet an old carburetor.