#geometry

#geometry

Squaring the Circle: Mathematicians Have Finally Solved the Ancient Math Problem of Turning a Circle into a Square (and Back)To this day, scientists are still figuring out whether it is possible to square a circle. The original question was by Anaxagoras of Clazomenae in 450 BC, who tried to square the circle using only classical tools, namely a straight edge and a compass, while in prison.In 1882, German mathematician Ferdinand von Lindemann proved that squaring the circle was impossible using only classical tools. Despite this, the question of squaring the circle remained a topic of interest for mathematicians.Recently, three mathematicians posted a paper online. Their study showed how to square the circle (and back) by cutting the circle into about 10^200 pieces (yes, that many). Another group of researchers also did the same thing back in 2016, but the shapes from this new paper are said to be "simpler in shape and much easier for mathematicians to visualize."Oleg Pikhurko, one of the study authors, says that he already has ideas to simplify and reduce the number of pieces needed to square the circle to less than 20 pieces.(Image Credit: Quanta Magazine)#Mathematics #SquaringTheCircle #Geometry #GraphTheory

Ancient Clay Tablet Showed that Applied Geometry was Used in Babylon 1,000 Years Before PythagorasAn ancient clay tablet that's been hiding in plain sight in the Istanbul Archaeological Museum in Turkey for over a century turned out to be the oldest example of applied geometry.The 3,700-year-old tablet known as Si.427 dated from the Old Babylonian period. "It’s the only known example of a cadastral document from the OB period, which is a plan used by surveyors to define land boundaries," said Daniel Mansfield of University of New South Wales in Australia. "In this case, it tells us legal and geometric details about a field that’s split after some of it was sold off," he added.The tablet uses number sets known as Pythagorean triplesto make accurate  right angles, but it was made 1,000 years before the Greek philosopher Pythagoras developed the geometric principles now known as the Pythagorean theorem.Image: University of New South Wales#math #mathematics #Babylon #claytablet #appliedgeometry #geometry #PythagoreanTriples #PythagoreanTheorem #landsurveyor

Morphing Pasta: Scientists Can Now "Program" Flat Pasta to Morph Into 3D Shapes When CookedBulky pasta like farfalle (fancy name for the bowtie pasta) and fusilli (the corkscrew pasta also called the rotini in the USA) require more packaging and take up more shelf space on the store than thinner varieties like spaghetti and angel hair pasta.But thanks to a new "morphing" techniques developed by researchers, that problem may be, ahem, licked once and for all!Led by researchers from the Morphing Matter Lab in Carnegie Mellon University, scientists can now "program" flat dough made from semolina flour into three-dimensional shaped pasta once boiled. They accomplish this by placing specific patterns of geometrical grooves or ridges on the pasta.With artificial intelligence, the scientists could even automate the process and make it easier for food manufacturers to create various shaped pasta for the consumers.#pasta #geometry #morphing #packaging #dough #semolinaflour #boiling #artificialintelligence #AI