Regular triangular tiling of the plane

The affine symmetric groups are a family of mathematical structures that describe the symmetries of the number line and the regular triangular tiling of the plane (pictured), as well as related higher- dimensional objects. They may also be defined as collections of permutations (rearrangements) of the integers that are periodic in a certain sense, or in purely algebraic terms as a group with certain generators and relations. They are studied in the fields of combinatorics and representation theory. Each of these groups is an infinite extension of a finite symmetric group, and many important combinatorial properties of the finite symmetric groups can be extended to the corresponding affine symmetric groups. The affine symmetric groups have close relationships with other mathematical objects, including juggling patterns and certain complex reflection groups. Many of their combinatorial and geometric properties extend to the broader family of affine Coxeter groups. ( Full article...)

Caricature of Harry Jackson

• ... that Harry Jackson (pictured) received acclaim for his portrayal of Napoleon due to his physical resemblance?
• ... that climate change protesters vandalized and glued themselves to a version of Andy Warhol's Campbell's Soup I?
• ... that Paul Roach became so popular for coaching the Wyoming Cowboys football team that people voted for him to be the state's governor even though he was not a candidate?
• ... that Angeline Quinto became the first Filipino singer to release a soundtrack album for a television series that featured a single artist?
• ... that the early big cat Pachypanthera may have weighed as much as 142 kilograms (313 lb) and had teeth similar to a hyena's?
• ... that in 2014, one could pay half a million US dollars to live in a former residence for people with tuberculosis?
• ... that when Jessica Berman was named the deputy commissioner of the National Lacrosse League, she became the first woman to hold that position in a men's professional sports league?
• ... that Venetian Blinds uses Venetian blinds to simulate Venetian blinds?

Rocket impact in Rishon LeZion

• Israel declares a state of war after Hamas and other Palestinian militant groups launch a series of attacks from the Gaza Strip that has left hundreds dead (aftermath pictured).
• Two earthquakes leave more than 2,000 people dead in Herat, Afghanistan.
• The Nobel Peace Prize is awarded to Narges Mohammadi "for her fight against the oppression of women in Iran and her fight to promote human rights and freedom for all".
• The Nobel Prize in Literature is awarded to Norwegian author and playwright Jon Fosse.

October 8

Fourth Ecumenical Council of Chalcedon by Vasily Surikov

• 451 – The Council of Chalcedon (depicted), a Christian ecumenical council, opened, and went on to repudiate the Eutychian doctrine of monophysitism and set forth the Chalcedonian Creed.
• 1918 – World War I: After his platoon suffered heavy casualties during the Meuse–Argonne offensive in France's Forest of Argonne, American Corporal Alvin York led the 7 remaining men on an attack against a German machine gun nest; 25 German soldiers were killed and 132 captured.
• 1932 – The Indian Air Force was founded as an auxiliary air force of the British Royal Air Force.
• 2016 – Yemen War: A funeral in Sanaa was hit by two consecutive airstrikes by a Saudi-led coalition, leaving 143–155 civilians dead and more than 525 injured.
• 2019 – Anti-government protests calling for free and fair elections began in Baku, Azerbaijan.