Trigonometry...Babylonians did it 1500 years before the Greeks

[LadyStanley]

https://www.upworthy.com/3700-year-old-babylonian-stone-tablet-gets-translated-changes-history-rp5

Using base-60 system.

Click to read more...

 

[JMCx4]

https://www.upworthy.com/3700-year-old-babylonian-stone-tablet-gets-translated-changes-history-rp5

Using base-60 system.

Sexagesimalism RULES!

 

[Hippasus]

https://www.upworthy.com/3700-year-old-babylonian-stone-tablet-gets-translated-changes-history-rp5

Using base-60 system.

I think the claim of this article is debatable. There are Pythagorean triples (a^2+b^2=c^2, with a,b,c integers), solutions of quadratic equations (cf. the quadratic formula), and trigonometric tables. The Wikipedia entry for Plimpton 322 states that researchers are unsure as to which of these three is inscribed into the artifact.

I think that although Pythagorean triples, and implicitly, quadratic equations, are built into the notion of trigonometric expressions, such as the formula for the chord of a circle, trigonometry proper is marked by tying triangles (e.g. the Pythagorean theorem) to circular forms (like the unit circle, and where angles come into play). The burden of proof is on the researchers mentioned in the article to show that the Pythagorean triples on Plimpton 322 in fact describe circular forms in the manner of veritable trigonometric tables such as has been ascribed to the works of Hipparchus from ancient Greece.

Nevertheless, the Babylonians were certainly pioneers in mathematics.

 

[JMCx4]

I think the claim of this article is debatable. ... The burden of proof is on the researchers mentioned in the article ...

Pending their next grant award.

 

[Nogatco Rd]

I think the claim of this article is debatable. There are Pythagorean triples (a^2+b^2=c^2, with a,b,c integers), solutions of quadratic equations (cf. the quadratic formula), and trigonometric tables. The Wikipedia entry for Plimpton 322 states that researchers are unsure as to which of these three is inscribed into the artifact.

I think that although Pythagorean triples, and implicitly, quadratic equations, are built into the notion of trigonometric expressions, such as the formula for the chord of a circle, trigonometry proper is marked by tying triangles (e.g. the Pythagorean theorem) to circular forms (like the unit circle, and where angles come into play). The burden of proof is on the researchers mentioned in the article to show that the Pythagorean triples on Plimpton 322 in fact describe circular forms in the manner of a veritable trigonometric tables such as has been ascribed to the works of Hipparchus from ancient Greece.

Nevertheless, the Babylonians were certainly pioneers in mathematics.

Now I’m intrigued with this sequence, what’s the significance?

1,9,45,165,495,1287,

 

[JMCx4]

Now I’m intrigued with this sequence, what’s the significance?

1,9,45,165,495,1287,

For me, it's that I'm gonna choose 1287 as my thrice-weekly Powerball pick through the end of the year.

 

[Hippasus]

Now I’m intrigued with this sequence, what’s the significance?

1,9,45,165,495,1287,

That is from an early attempt of mine to solve a discrete mathematics and combinatorics problem that I thought about several years ago in connection with an advertisement I heard. I still have my notes on it.

Circa 2010 in Canada, there was a Dairy Queen commercial that said one can have pairs, triples, or quadruples from a choice of nine items. The claim was this number exceeded 20,000 possibilities. I thought this to be a gross overestimate and tried to come up with a systematic way of tallying the actual numbers in the sequence.

Say there are nine possible side items to choose from. Order of selection does not matter, repetition matters (we can select the same combo item repeatedly).

First element in the sequence: Say one has no choice in the matter. "You may select nothing." There is one possibility of zero items selected.

Second element in the sequence: Say one has one choice. There are nine possibilities.

Third element in the sequence: Say one has two choices. These are the possible pairs, of which there are forty-five possibilities:
11 22 33 44 55 66 77 88 99
12 23 34 45 56 67 78 89
13 24 35 46 57 68 79
14 25 36 47 58 59
15 26 37 48 59
16 27 38 49
17 28 39
18 29
19.

(2+9-1)! / (2!(9-2)!) = 45 (n=9, r=2).

Fourth element in the sequence: triples. Say one has three possibilities. Then: 165.

Fifth element in the sequence: quadruples. Say one has four possible selections. Then: 495.

Sixth element in the sequence: quintuples. So there are five selections we can make in this case. Then: 1287.

The triangular pattern when I tried to count it by brute force is interesting, and the formula corroborates the entries. It is actually an infinite sequence.

In short, the Dairy Queen commercial was far off, and that was false advertising. 45+165+495=705. This is far shy of "over 20,000 possibilities".

 

[JMCx4]

That is from an early attempt of mine to solve a discrete mathematics and combinatorics problem that I thought about several years ago in connection with an advertisement I heard. I still have my notes on it.

Circa 2010 in Canada, there was a Dairy Queen commercial that said you can have pairs, triples, or quadruples from a choice of nine items. The claim was this number exceeded 20,000 possibilities. I thought this to be a gross overestimate and tried to come up with a systematic way of tallying the actual numbers in the sequence. ...

In short, the Dairy Queen commercial was far off, and that was false advertising. 45+165+495=705. This is far shy of "over 20,000 possibilities".

Be sure to add: "MUCH smarter than Dairy Queen (and their marketing partner)" to your resume.