## Wednesday, August 30, 2017

### Ancient Babylonians Did Trigonometry

This is WAY cool!  From The New York Times:

# Hints of Trigonometry on a 3,700-Year-Old Babylonian Tablet

By Kenneth Chang August 29, 2017

Suppose that a ramp leading to the top of a ziggurat wall is 56 cubits long, and the vertical height of the ziggurat is 45 cubits. What is the distance x from the outside base of the ramp to the point directly below the top? (Ziggurats were terraced pyramids built in the ancient Middle East; a cubit is a length of measure equal to about 18 inches or 44 centimeters.)

Could the Babylonians who lived in what is now Iraq more than 3,700 years ago solve a word problem like this?

Two Australian mathematicians assert that an ancient clay tablet was a tool for working out trigonometry problems, possibly adding to the many techniques that Babylonian mathematicians had mastered.

 An ancient Babylonian tablet known as Plimpton 322 consists of a table of 60 numbers organized into 15 rows and four columns.CreditAndrew Kelly/University of New South Wales
“It’s a trigonometric table, which is 3,000 years ahead of its time,” said Daniel F. Mansfield of the University of New South Wales. Dr. Mansfield and his colleague Norman J. Wildberger reported their findings last week in the journal Historia Mathematica.

Rest of article.

Sadly, I could not make heads nor tails out of the word problem as I did not think I had enough information to solve what I understood the problem to be asking for.  However, what the article says is that it was a simple calculation of the length of the third side of a right triangle when we had the measurement for the other two sides.  Even I remember how to solve for any side of a right triangle if I have the two other numbers from high school trig, taken eons ago.  Really - that is what the word problem is asking me to solve for?  The way I read this problem, it was asking for the actual length of the ramp as measured on its outermost edge from its beginning (pick a corner, any corner, and go around each level upward from there) up to the point (how do you determine what "point?") just below the peak of the structure.  I did not read this to be a simple solve for "b" in "a squared" + "b squared" = "c squared."  LOL!  Silly me.  No wonder parents can't help their kids with this new math these days, geez!  Its indecipherable!  Who wrote that problem - is English their third or fourth language?