Trig Warning: 3700-Year-Old Babylonian Tablet

     A Babylonian clay tablet known as Plimpton 322 was discovered early in the 20th century in present-day Iraq. An Australian mathematician, Dr. David Mansfield, who has been analyzing its meaning, announced his conclusions in late August, 2017, saying that "cracking the meaning of the tablet, as big as the palm of a human hand, could simplify our study of triangles."


      Up to now, trigonometry has been based on study of angles and irrational numbers. The analysis of Plimpton 322 reveals that the Babylonians used ratios during 2800 to 1700 BC.  “This gives us a different way of looking at trigonometry,” Dr. Mansfield said. “The beautiful thing about it is that it’s much simpler.” 


      "Trigonometry is not a fusty, {I find the use of the word"fusty" is awesome here!} esoteric branch of mathematics. It is essential to architecture, engineering, astronomy, surveying, and even oceanography. Up to now, it’s been taught using Greek principles. But this tablet proves that the Babylonians beat the Greeks in the discovery of trigonometry by about 1,000 years."

       The tablet was unearthed in southern Iraq, believed to be near the onetime Sumerian city of Larsa, by Edgar Banks, a collector of antiquities in the 1890s. Banks was not collecting cuneiform tablets as an archaeologist, but while using his position as the American consul to Baghdad. He sold the tablets to universities, libraries, and museums.

      "The Greek astronomer Hipparchus has been considered the father of trigonometry. But this tablet was created long before Hipparchus lived."

      Dr. Mansfield said, “Babylonian mathematics may have been out of fashion for more than 3,000 years but it has possible practical applications in surveying, computer graphics and education.”


      "The tablet got its name because an American publisher and collector named George Arthur Plimpton bought it. (He is the grandfather of writer and editor George Plimpton, founder of the Paris Review and author of Paper Lion.) In 1936, not long before he died, Plimpton donated the Babylonian tablet along with many other manuscripts to Columbia University."

     "In the 1940s, researchers who were studying the tablet concluded that the cuneiform numbers on it corresponded to the Pythagorean Theorem. But that was far as they got until Dr. Mansfield and his team took up the challenge.

      The tablet “is a fascinating mathematical work that demonstrates undoubted genius,” says Dr. Mansfield. “The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry.”

Not at all a fusty fuss, eh?
Steph

Elk in downtown Evergreen, CO >>>



LIDAR, Connecticut Forests, and Iowa Marching Bear Effigy Mounds

       Dr. Katharine Johnson from the University of Connecticut (UConn) focuses on uncovering  
hidden remnants of the past using LIDAR imaging. The name LIDAR, sometimes considered an acronym of Light Detection And Ranging (sometimes Light Imaging, Detection, And Ranging), was originally a portmanteau of light and radar. Johnson and her colleagues have been piercing dense forest cover to uncover historic sites in New England (as seen here in Plainfield, Connecticut).

      

     Many of the tree-covered landscapes of modern New England were not always so green. In the 17th century, the region was the site of widespread deforestation, as European colonists built farms and homesteads. Between 60 to 80 percent of the land was cleared for fields, pastures, and orchards; these were surrounded with stone walls, houses, outbuildings, and roads.

      The natural-color photograph above was shot during an aerial survey in 2012. The monochromatic light detection and ranging (LIDAR) image, captured in 2010, shows the same area with greater contrast and reveals features on the ground. 

      LIDAR instruments send out rapid pulses of laser light that reflect off of solid surfaces (such as tree limbs or the ground). A receiver detects the photons that bounce back to the instrument, parsing out subtle variations in land elevation and allowing researchers to distinguish bumps and surfaces on the terrain.

      LIDAR has been used by archaeologists in other landscapes, perhaps most famously in Belize, where researchers have used it to uncover ancient Maya sites. The startling Marching Bear Effigy Mounds in northeastern Iowa were highlighted with LIDAR as well.

        

     “You can see patterns people made as they were dividing the landscape and farming,” said Johnson. LIDAR imaging helped them uncover traces of stone walls, dams, abandoned roads, building foundations, farm structures, and relict charcoal hearths—all of which have been slowly hidden over the past two centuries as the forest reclaimed the land.

 “The biggest surprise was being able to see the extent to which historic land use had impacted the landscape, which is not something that is readily visible in high-resolution aerial photos.”

Happy 24th birthday to Zoë today! Here she is celebrating with fellow Peace Corps volunteers in Ethiopia.

Have you used LIDAR?
Steph

Eclipse photos. Moonshadow. Moonshadow. . .How was your solar eclipse experience?

Eclipse at the Great Sand Dunes, Colorado--whoa!

Crinoids for Cri-nerds

     We discussed crinoids,

also known as sea "lilies," here at Partial Ellipsis of the Sun in April. This extraordinarily well-preserved Paleozoic crinoid fossil sample (below) inspired another look at this animal that looks like a plant.

      Compare the sample above to the "Smarties" stem pieces we found in northern Arkansas in April. The disarticulated crinoid stems or stalks are relatively common, but the delicate, lacy crown pieces are much rarer.

      Modern day crinoids and the fossil animals are quite similar, hence they are often referred to by the non-scientific term "living fossils."

       The parts of crinoid animals are labelled below, though the terms are quite plant-based:

I guess you could say I'm a bit of a cri-nerd ;-).

     How about you?
     Steph