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In 1852 a South African mathematician asked a seemingly simple question that triggered endless dispute, left a trail of overturned publications in its wake and culminated in a resolution that has stretched the very tenets of math. The color conundrum that stirred up so much trouble: What is the fewest number of colors needed to color a map so that no neighboring states or other designated areas have the same hue? Here’s how it works. Check out the map of the contiguous U.S. below. Credit: June…

Despite featuring many of the same weapon types, different games have varied ways of tackling how each of them works and feels. Sometimes this evolves through sequels, which is clearly evident when looking how how bows worked between The Last of Us and The Last of Us Part II. The decisions that lead to this change were numerous, according to a senior game designer at Naughty Dog, who has broken down exactly how it works.In an enlightening thread on Twitter, designer Derek Mattson made the distinction…

Newton Raphson Method or Newton Method is a powerful technique for solving equations numerically. It is most commonly used for approximation of the roots of the real-valued functions. Newton Rapson Method was developed by Isaac Newton and Joseph Raphson, hence the name Newton Rapson Method. Newton Raphson Method involves iteratively refining an initial guess to converge it toward the desired root. However, the method is not efficient to calculate the roots of the polynomials or equations with higher degrees but in the…

In a pale world of ice and snow, the last color you expect to see on the horizon is red.In 1911, during a British expedition to Antarctica, researchers were shocked to notice a glacier 'bleeding' from its tongue onto an ice-covered lake.The crimson drool is known as Blood Falls, and it's taken experts more than a century to figure out what is actually causing the eerie coloring.When a team of US scientists took samples from Taylor Glacier's rusty tongue in November 2006 and mid and late November 2018, and analyzed the…

Ken Livi, a researcher at Johns Hopkins University, may have finally discovered the secret behind the mysterious “Blood Falls” of Taylor Glacier in Antarctica. Discovered over 100 years ago during the infamous Terra Nova Expedition to Antarctica in 1911, the “Blood Falls” were named after the bright red water that seems to flow from the falls. While many believed that the falls acquired this red color due to minerals in the water, new research on samples taken from the fall point towards a much different…

Optical illusions are tricky little things. Often they can leave us scratching our heads, trying to figure out how the illusion is tricking our eyes and our brain. One type of illusion, known as a “simultaneous contrast illusion,” may finally have an explanation, though, according to a new study. See that image at the top of the article? While it might seem like the gray rectangle in the middle is composed of two different colors at first glance, it’s actually just one color, though it appears to be two…

Credit: CC0 Public Domain Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title "On the invariant subspace problem in Hilbert spaces." The paper is just 13 pages long and its list of references contains only a single entry. The paper purports to contain the final piece of a jigsaw…

Tigers may not change their stripes, but Jupiter sure does. The giant planet's surprisingly neat, alternating bands of dark and light clouds periodically change their appearance, but the reason for these cyclic variations is a mystery.Now, after studying data on Jupiter's magnetic field collected by the Juno probe, a team of scientists from Japan, Spain, and the UK think they've cracked it. The changes seen in Jupiter's stripes coincide with magnetic oscillations inside the gas world."It is possible to get wavelike…

Images from a ground-based infra-red telescope, showing Jupiter at 5 micron wavelength radiation. The remarkable change between May 2001 and December 2011 in the North Equatorial Belt (highlighted between the dashed blue lines) can be seen. Credit: Arrate Antuñano/NASA/IRTF/NSFCam/SpeXResearchers have used <span class="glossaryLink" aria-describedby="tt" data-cmtooltip="<div class=glossaryItemTitle>NASA</div><div class=glossaryItemBody>Established in 1958, the National…

This is an artist’s impression of a runaway supermassive black hole. Researchers at the IAC have discovered that an unusual thin structure of stars might actually be a galaxy seen edge-on, rather than a trail left by a fleeing supermassive black hole. Credit: NASA, ESA, Leah Hustak (STScI)A study carried out by a team of researchers at the Instituto de Astrofísica de Canarias (IAC) has shown that an unusually thin structure of stars, recently discovered by the <span class="glossaryLink"…