An implication of Albert Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only over short distances (relative to the strength of the gravitational field). Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. įor more than two thousand years, the adjective "Euclidean" was unnecessary becauseĮuclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that theorems proved from them were deemed absolutely true, and thus no other sorts of geometry were possible. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language. It goes on to the solid geometry of three dimensions. The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions ( theorems) from these. 64:1 (2020), 63-108.Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Springborn, Ideal hyperbolic polyhedra and discrete uniformization, Discrete Comput. Crane, Conformal geometry of simplicial surfaces, in: Proceedings of Symposia inī. Hyperbolic geometry of Markov's theorem on DiophantineĪpproximation and quadratic forms, Enseign. Aigner, Markov's theorem and 100 years of the uniqueness conjecture: a mathematical journey from irrational numbers to perfect matchings, Springer, 2013. Quadratic forms, Diophantine approximation and the hyperbolic geometry of numbers.Bonahon, Low-Dimensional Geometry: From Euclidean Surfaces to Hyperbolic Knots, AMS, 2009 Milnor, Hyperbolic Geometry: The first 150į. Of Geometry, MSRI Publications 31, Cambridge University Encyclopedia of Mathematical Sciences 29. Surface with ideal vertices in hyperbolic 3-space.ĭ. Hyperbolic metric on a punctured surface as a convex polyhedral Theĭiscrete uniformization problem for polyhedral surfaces turns out toīe equivalent to the following problem: to realize a given complete This theory isīest understood using three-dimensional hyperbolic geometry. With polyhedral surfaces instead of Riemann surfaces. The Euclidean plane, or the hyperbolic plane by the action of aĭiscrete group of isometries. Riemann surface is conformally equivalent to quotient of the sphere, The Uniformization Theorem of complex analysis says that every compact On how far these geodesics stay away from Triangulation, and how well a number can be approximated depends From this point of view,Ĭontinued fractions describe the paths of geodesics in Treat this subject using hyperbolic geometry. Classically, the principal tool in thisĪrea of Diophantine approximation are continued fractions. The very worst classes form an infinite sequence, the Numbers represents a class of equally badly approximable To be the golden ratio (1+√5)/2, followed by √2, and The very worst approximable irrational number turns out Some irrational numbers are better approximated by rational numbers The course is mainly about two topics where hyperbolic geometry is useful for something else. Formalitiesįortgeschrittene Themen der Differentialgeometrie, Please write me an email with your personal data (name, Studiengang, or whatever is appropriate) to register. BlogĪfter the lectures, I will post the blackboards in the course blog, which is also a good place for comments, questions and discussion. Since it turned out that everybody speaks German, the lectures are in German. Mondays & Thursdays at 10:15-11:45 via Zoom (see blog) Sommer 2021 Applications of Hyperbolic Geometry Boris Springborn Lectures Fortgeschrittene Themen der Differentialgeometrie
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With her acting skills, the well-known Asian beauty has won the hearts of both children and adults. Later in September 2015, Keiko launched Drunk Monk Podcast with individual comedy comic Will S. In 2002, she received an Emmy Award and a Young Artist Award for her work on Lil Tokyo Reporter. On the enlivened arrangement “Kim Possible,” she voiced Yori. She was nominated for Teen Choice Awards in 2001, 2002, and 2003 solely for her role in Gilmore Girls. She got her big break as Lane Kim in the show Gilmore Girls.įrom 2000 to 2007, the actress was the main character in the arrangement. From then on, she appeared in a few TV movies, including Sister, Sister, ER, Beverly Hills, 90210, and Felicity. In 1993, she made her acting debut as Mitsuko in a scene from the TV series Renegade. Keiko began her age as an entertainer when she was 10 years old. Her bra size is 32B, her shoe size is 6 US, and her dress size is 2-4. Keiko stands 5 feet 1 inch tall and weighs 54 kg. It appears she is doing the best she can without causing harm to others and has been a straight individual her entire life, for which she has not been in any contention. There are currently no frantic tidbits of gossip about her personal or professional life. While there is no information about her salary. Estimated Net Worth of Keiko AgenaĪs a result, the actress’s net worth is estimated to be $300,000 USD. They have been married for over 12 years and are very happy. However, Shin Kawasaki, Keiko’s husband, is a talented musician who has had a passion for music from a young age. Their unique and iconic wedding marked the beginning of a beautiful journey. Their wedding was an unforgettable event. The couple appears to be doing well, as there has been no mention of marital problems in the sensationalist press. Februin Biography Keiko Agena and Shin Kawasaki were married and tied the knot on December 19, 2005. However, no news about her pregnancy has emerged. Their wedding reception was held in Las Vegas, Nevada. She married her long-term boyfriend, Shin Kawasaki. In terms of her educational background, she attended the Mid-Pacific Institute private academy on O’ahu and Whitman College for one year as a show major. She began acting when she was ten years old. Her mother’s name is Claire Agena, and her father’s name is unknown. The actress was born on October 3, 1973, in Honolulu, Hawaii, USA. Pipedream is a low code integration platform for developers, which helps to connect APIs fast. Bring Trello into your Google App Trello Add-on for Gmail Make emails do things with Trello actions in Gmail. Now they can track time from the Trello cards where theyre already. Live chat support and an impressive 10k+ customer base set it apart. Make time tracking easier on your team by bringing Harvest timers directly into Trello. Integrately helps to integrate your apps in 1 click using easy to set up automation templates. App Integrations Trello + Asana app integration: Sync Trello and Asana Trello + Asana Integrate Asana with Trello and automatically sync cards, tasks, projects, boards, comments, assignees, custom fields, and more. Choose from multiple integrations to streamline your team's efforts and increase productivity. Sign in to Trello and have Trello automatically generate an application key. With two-way syncing, updates between tools are reflected in real-time. Set up a Trello problem-notification integration to keep you updated on all. Simplest Mac app for creating timesheets. Add Detectify security notifications to your favourite to-do list. Unito is a top-tier, no-code integration solution that enables seamless workflows across multiple apps. DAKboard is a connected display for photos, calendar, weather, news and Trello boards Embed interactive. For more information, check out this article on Trello integration. Microsoft Power Automate, previously Microsoft Flow, helps to improve productivity using business process automation with triggers and actions. Import your Trello data to Forecasts comprehensive platform. Link your Slack and Trello workspaces to build the ultimate productivity powerhouse. With over 5,000 popular apps connected, it's never been easier to streamline your workflow. Go to Settings > Apps, click on the Trello integration then select Remove account. Zapier simplifies busy people's lives by automating web app data transfers, reducing tedious tasks, and allowing teams to collaborate effortlessly. Track all the Trello cards you work on from your Memory Timeline. Explore this list to find the best fit for your business. Trello’s boards, lists and cards enable you to organize and prioritize your personal and work life in a fun, flexible and rewarding way. Integrate with Atlassian apps and many others. The fun & flexible way to get more done and connect your team.
Discover a few styles below and add them to your wardrobe!įormal dresses: Do you tend to dress down at formal events, making your party dress work when everybody else is wearing floor-length gowns and beaded overlays? Splurge a little on a new evening dress - if you’re not a big event person, make it last the distance by checking out timeless cuts and colours (a black dress is always in fashion).Įnter the bodycon dress: Bodycon dresses can be a tall order if you’re not accustomed to showing off some curve, but they have the potential to suit every shape and size, with or without shapewear. While we all want to turn heads, the only opinion that really matters is yours - what makes you feel confident? When do you feel your most comfortable? Maybe it’s time for something new, or maybe a fresh take on an old favourite is the best plan. When was the last time you wore a midi dress and felt good? Own your clothing confidence again and stock your wardrobe with comment worthy summer dresses, flowing maxi dresses and event-ready cocktail dresses. Delivering a carefully curated range of dresses Australia wide, we’re proud to offer a combination of local brands, emerging designers, international names and powerhouse icons, ensuring we remain your one-stop dress destination for every occasion.īut let’s talk about you. Dresses have hidden powers, working their magic on your overall confidence as you step out the door ready to take on the world, styled by our collection of women’s dresses. In another, Rue’s best friend and love interest, Jules (played by incredible newcomer Hunter Schafer), doodles gigantic starbursts on the corners of her eyes and goes roller-skating. In one scene, Zendaya’s protagonist, Rue, paints glittery golden triangles underneath her eyes and heads to a local carnival. I’ve never seen anything like it, and I think about it eight times per day. Like the show itself, the eye makeup on Euphoria is unhinged and gorgeous. I love it! But I often have a hard time trying to figure out whether the show is meant to be a genuine reflection of the Gen Z experience, or a sort of elevated, Hunter S. MUA Discord Different mod team to reddit MUA.The primary function of Euphoria - HBO’s new drama starring Zendaya as a drug addict with incredible skin - seems to be to make adults pause and ask, “Wait … are the teens … okay?” It’s the sort of show that begs to be described as “gritty,” painting a rather stark portrait of Gen Z as a bunch of nudes-crazed, molly-popping depressives who mount each other in pools and have public orgasms atop carousels.Shopping Guides: MUA's Favorite Products.Violations of rules will result in your post being removed. Moderators reserve the right to make decisions deemed to be in the best interest of the subreddit. You may post images that are not yours for inspiration purposes, but they must follow the rest of the rules about photos and you must provide the source and clearly mark that you are not the creator. All Haul posts must include swatches and/ or a mini review of at least 3 products. No referral links, surveys, giveaways, or seeking to buy or sell!Įxcept during Friday Faves, remove products from packaging and open the product itself before posting. Limited linking in comments is acceptable. No self-promotion of Youtube/social media/blogs/your business in your post title. Request exemption in modmail prior to posting if needed.Īll fake blood/injuries must be marked NSFW. List must be placed as a top-level comment. Product lists must include shade names if they exist. All makeup looks and collections must include a detailed product list in a top-level comment which includes every product used in the visible area, including even invisible products like primer and setting sprays. "Selfie Angles" are strongly discouraged. Images where the makeup cannot be seen well or the quality is too low for constructive criticism will be removed. Photo Quality and Composition: All photos must showcase the makeup clearly and be properly cropped. "No Makeup Makeup" looks or other looks where the makeup is too subtle to see easily must have a before and after shot so users can see the difference the makeup makes. Read our photo guidelines before you post! This includes any photo alterations such as beauty filters, portrait modes, sharpening, contrast alteration, artificial bokeh, text overlays, and all but the most minor color corrections. Content implying requests for sympathy may also be removed. Post titles, descriptions, and comments must also not be self-deprecating, self-disparaging, or otherwise unkind in tone. Constructive criticism is strongly encouraged, but it is not allowed on some types of posts. No harassment or name calling, bigotry, or self-deprecation.
Staff Sergeant Vernell Robinson Jr., "was convicted of 19 counts involving the abuse of five women under his command," including sodomy, adultery, communicating a threat, obstructing justice and disobeying orders.He was convicted of 18 counts of rape and 29 other offenses, and was sentenced to 25 years in military prison. Sergeant Delmar Simpson was held at the Marine Corps Brig, Quantico while his court-martial was pending.However, she did order prospective jurors not to follow media coverage of the case to avoid interference with their judgment. Robertson's attorney, Jerome Murphy, asked the military judge Linda Webster, to enact a gag order on West and others, but she deferred judgment. The men accused felt that statements made by West and other officials within the Army were prejudging the case and would result in an unfair trial. Īrmy Secretary Togo West accused those charged of abusing their power, and ordered all soldiers to undergo sexual harassment training so they could learn the Army's " zero tolerance" policy towards sexual harassment. Robertson and Simpson faced rape charges and Beech was charged with adultery. Additionally, "letters of reprimand were issued to Aberdeen's commanding general and three other senior officers." Charges brought against the officers Ĭaptain Derrick Robertson and Sergeants Delmar Simpson and Nathanael Beech were accused of participating in the Army's biggest sex abuse scandal on record. Ultimately, twelve drill instructors were charged with sex crimes four were sentenced to prison, while eight others were discharged or received non-judicial punishment. The Aberdeen Scandal was a military sexual assault scandal in 1996 at Aberdeen Proving Ground, a United States Army base in Maryland. JSTOR ( November 2014) ( Learn how and when to remove this template message).Unsourced material may be challenged and removed. Please help improve this article by adding citations to reliable sources. This article needs additional citations for verification. A supernova within our galaxy is a once in a lifetime spectacle', tweeted physics teacher Dr David Boyce.īetelgeuse is a red supergiant star that is about 1,400 times larger than the sun, according to the European Southern Observatory. 'Whatever happens it will be worth watching. The last time a nearby supernova was visible from Earth was in 1987, that star was in the Large Magellanic Cloud about 168,000 light years away - Betelgeuse is 700 light years away so its explosion would be much brighter. Science writer, Jason Major, says it is unlikely to happen but speculating about the idea of a nearby supernova for scientists is like 'imagining what you'd do with the money if you won the lottery'. 'The statistical likelihood of this event occurring during your 90 (give or a take a few years) year lifetime is extremely small.' The whole process will release 100 times as much energy as our Sun will during its 10-billion-year lifetime and leave behind an exotic remnant, a black hole or neutron star.Betelgeuse will explode - it's just a matter of when - it’s at the end of its life and is due to end in a supernova event, astronomer Dave Eagle explained. Reactions continue, but they sap the star of energy and throw off the balance between expansion and gravitational contraction, causing the star to collapse in on itself and trigger a staggering explosion, a supernova.Īs the core collapses, it sends out a shock wave that compresses the surrounding stellar materials, making rare elements such as silver, tin, gold, uranium, mercury and zinc. Read More: This is What a Black Hole Sounds Like Fusion will create oxygen, neon, silicon and finally iron, which accumulates in a huge core. These reactions release large amounts of energy and send many, many photons out into the universe, including those that reached Moore’s eyes.īetelgeuse’s next stages will happen quicker as its temperatures rise, sending the star down a slippery slope. Starting with hydrogen, which it’s already fused into helium, the fuel for its current stage will make carbon. Read More: What Happens When a Star Dies?Īs a massive star, Betelgeuse is expected to go through a dramatic end-of-life catastrophe that will produce either a neutron star or black hole and likely a show for any surviving observers on earth.īefore the catastrophe, Betelgeuse must burn through several different types of nuclear fuel. "Betelgeuse is not at all close to exploding," a press release said, and what's more, the star "is too far from Earth for the eventual explosion to have significant impact here." When researchers from the Kavli Institute for the Physics and Mathematics of the Universe, in Japan, analyzed Betelgeuse in 2020, they concluded that the star was still early in its helium-burning phase. But scientists have said such an event will probably take another 10,000 to 100,000 years. Brightening in recent weeks has even raised alarm that the aging star, positioned about 650 light years from Earth, could blast itself apart in a supernova, one of the most violent events in the universe. In more recent years, the star has traded in its steady, 400-day cycle of glaring and quieting for something much shorter and more spasmodic. The sun has often ejected small amounts of material in a similar fashion, called a coronal mass ejection (CME), but the Betelgeuse belch was 400 billion times larger than the average CME. On the uppermost level, the scarred surface is bouncing around “like a plate of gelatin dessert.” Its internal convection cells, which normally drive its characteristic brightening and dimming, are now sloshing around like an unbalanced washing machine, NASA says. Backyard observers around the world noticed the change, which lasted a few months.Īfter its dramatic vomiting, Betelgeuse fell into a period of turbulence expected to continue for at least another year or two. The ejected material, which weighed several times as much as our moon, cooled out in space, where it blocked light from reaching earth and darkened Moore’s star dramatically in what became known as The Great Dimming. In 2019, a powerful plume rose up from inside it, NASA has hypothesized, and blasted off a chunk of the star’s outer layer. What is Betelgeuse?īetelgeuse is a massive star, about 700 times the size of the sun. And since Moore died in 2012, things have only gotten worse. Click the menu button in the top left corner of Opera, select Extensions in the drop-down menu and choose Get extensions.ģ. Note: The name of the selection option will be different with translators, but it always begins with Translate page.Ģ. Right-click the web page that you want to translate and select Translate page with Google Translate. Tap Add when a pop-out window is shown under the address bar to ask for permission.Ħ. Click the translator that you like and tap. Select Extensions in the left panel of the Firefox add-ons page and type translator in the search box.Ĥ. Click the Open menu in the upper right corner of Firefox and select Add-ons option in the drop-down menu.ģ. Then choose the language you need and tap Translate to finish.Ģ. Note: If you want to change the language, you can click the translation icon in the address bar and choose Change languages after selecting Options. Right-click the web page that you want to translate. Note: You can add translated language here.Ĥ. Find Language options under the Advanced section and turn on the translation button if it is turned off. Click the menu button in the upper right corner of Chrome and select Settings in the drop-down menu.ģ. And here are ways for three popular browsers to translate web pages directly. Instead of copying the web page content and pasting it in the translator, it's more convenient that there is a translation feature in the browser. Sometimes, we may want to translate the web page which is displayed in an unfamiliar language, or we want to translate the language of the web page into a language that we are learning. How to Translate Web Pages in Chrome, Firefox or Opera The Nor’easters also won the ICCA Wildcard Championship in 2015. They were named champions of the International Championship of Collegiate A Cappella (ICCA) in 20. Northeastern University’s premier co-ed a cappella group, Nor’easters, is the oldest a capella group on campus. Another co-ed a cappella group which was founded in 2015, Upper Structure, placed 2nd place in the 2018 ICCA Final and was featured on the Best of Collegiate A Cappella (BOCA) 2018 album. Of these, Upper Structure is striking a unique chord with the a cappella world. Berklee is the home to four other a cappella groups: CharlieChords, On the Vox, Treble Threat and Upper Structure. Pitch Slapped also appeared on NBC’s The Sing Off and was featured on America’s Got Talent in 2015. According to the Pitch Slapped website, the group has been named one of the top five a cappella groups in the country by USA Today, won two International Championship of Collegiate A Cappella competitions in 20. Pitch Slapped was founded in 2006 and, in the last twelve years has made more than just a name for itself. It comes as no surprise that “the largest independent college of contemporary music in the world” should also produce some stunning a capella groups. _ Berklee College of Music Pitch Slapped & Upper Structure This article includes 20 of the most outstanding collegiate a cappella groups, old and new, who have resonated with audiences around the world. Today, a cappella groups in colleges number over twelve hundred according to some estimates. However, a cappella, as vocal music sung with no instruments at all, must be one of the oldest forms of music around. The origins of collegiate a cappella are nebulous, the oldest known collegiate a cappella group being the RPI Glee Club of Rensselaer Polytechnic Institute, established in 1873. A cappella groups associated with a college are not usually directly affiliated with the school’s music program, but are most often directed and operated by the students. Collegiate a cappella groups, according to Wikipedia, usually perform a pop-centric music genre. A cappella music is performed by singers without any musical instruments. Auction price list for Opus One : Wine Value. The result is the wine that represents Napa Valley to the world-and is sure tol be a centerpiece in any collection. Opus One (United-States California): guide, presentation, price estimates and. They show up at 3 am, night after night, when it’s time to harvest, and masterfully translate that into the bottle. Over the last 30 years, the carefully chosen Opus One team has mapped the wine’s vineyards down to each individual vine. Even after tasting legendary vintages like 20, we couldn’t stop raving about the 2016. Opus One has a remarkable throughline of pitch-perfect quality and complexity that we rarely see replicated in Napa, Bordeaux, or beyond. Our tasting of nearly a dozen vintages highlighted the wine’s exquisite and graceful ageability. Opening, pouring, and indulging in Opus One is a singular pleasure. It’s full-bodied, opulent, and impeccably balanced. We fell in love with its plush mouthfeel, which is dominated by blackberry and cassis that coat the mouth with a creamy texture before accents of sage, black olives, dark chocolate, and espresso emerge. In the glass, it boasts an inky ruby hue with elegant and polished aromas of crushed red and blue fruit, baking spice, and woodsy herbs. James Suckling honored their 2016 release with a near-perfect 99-point score, calling the 2016 “complex and complete.” Robert Parker’s Wine Advocate gave the 2016 98 points, praising the wine’s dense palate as a “tightly coiled spring ready to explode.” The legendary partnership between Bordeaux First Growth Mouton Rothschild and Robert Mondavi solidified Napa as a powerhouse wine region and global leader in modern winemaking. |
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