![]() Many mathematicians have since searched for the single-tile solution, the “einstein,” but none had succeeded-including Penrose, who eventually turned his attention to other puzzles. The famous, elegant Penrose tiling uses just two types of tiles to make an aperiodic pattern. Credit: Inductiveload/Wikipedia Three years later mathematician Raphael Robinson found a variant with only six tile types-and finally, in 1974, physicist Roger Penrose presented a solution with only two tiles. Then, in 1968, computer scientist Donald Knuth found an example with 92. First, Berger found one with 104 different tiles. ![]() In the decades that followed, mathematicians found smaller and smaller sets of tiles that can create aperiodic mosaics. This discovery raised another question that has dogged mathematicians ever since: What is the minimum number of tile shapes that together can create an aperiodic tessellation? How Low Can You Go? And even better, it is physically impossible to form a repeating pattern with that set of tiles, no matter how you lay them. In his work, Berger found an unbelievably large set of 20,426 differently colored tiles that can pave a plane without the color pattern ever repeating itself. The culprit: the unpredictable, nonrepeating nature of aperiodic tilings. There will always be cases where you can’t predict whether you can cover the surface without gaps. A mathematician would look at your game and ask, “Can you determine whether you will hit a dead end just by looking at the types of colored tiles you were given at the start? This would certainly save you a lot of time.” An aperiodic mosaic. Credit: Claudio Rocchini/Wikimedia (CC BY-SA 3.0) For example, maybe you needed just one tile in which all the edges were the same color. Game over.īut certainly, if you had the right tile with the right color combination, you could have gotten out of your pickle. There’s a gap you just can’t fill with the tiles you have available, and you are forced to place mismatched edges next to each other. You find a strategy you think is going to work, but at some point, you run into a dead end. With infinite tiles, you begin laying down pieces. You have to follow one rule, however: the edges of the tiles are colored, and only same-colored edges can touch. Suppose you want to tile an infinite surface with an infinite number of square tiles. Can you create an infinite mosaic with only same-color edges touching? Credit: Anomie/Wikimedia But such beauty harbors unanswerable questions-ones that are, as mathematician Robert Berger stated in 1966, provably unprovable. From Beautiful Patterns to Unprovable QuestionsĪnyone who has walked through the breathtaking mosaic corridors of the palace Alhambra in Granada, Spain, knows the artistry involved in tiling a plane. The team recently reported its results in a paper that was posted to the preprint server and has not yet been peer-reviewed. Even better, they found that Smith had discovered not only one but an infinite number of einstein tiles. Together with software developer Joseph Samuel Myers and mathematician Chaim Goodman-Strauss of the University of Arkansas, Kaplan proved that Smith’s singular tile does indeed pave the plane without gaps and without repetition. When he told Craig Kaplan, a computer scientist at the University of Waterloo in Ontario, Kaplan quickly recognized the potential of the shape. He discovered a 13-sided, craggy shape that he believed could be an einstein tile. Then, last November, retired printing systems engineer David Smith of Yorkshire, England, had a breakthrough. Many mathematicians had already given up hope of finding a solution with one tile, called the elusive “einstein” tile, which gets its name from the German words for “one stone.” Until now, aperiodic tilings always required at least two tiles of different shapes. No matter how you chop up the mosaic, each section will be unique. In these special cases, called aperiodic tilings, there’s no pattern that you can copy and paste to keep the tiling going. Specifically, mathematicians are interested in tile shapes that can cover the whole plane without ever creating a repeating design. For centuries, experts have been studying the special properties of tile shapes that can cover floors, kitchen backsplashes or infinitely large planes without leaving any gaps. It is also one of the hardest problems in mathematics. Creatively tiling a bathroom floor isn’t just a stressful task for DIY home renovators.
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![]() The album version runs 9:08, with the last lyric uttered at 4:55 (“fly high, free bird, yeah”). The opening lines, “If I leave here tomorrow, would you still remember me?” were inspired by Allen Collins’ girlfriend Kathy, who had asked him this very question during a fight. The lyrics are about a man explaining to a girl why he can’t settle down and make a commitment. If you can get through that one you’ve had a good night at a Skynyrd show.” Of course at the end it was dedicated to Duane Allman from the band Allman Brothers because it goes into the guitar part. ![]() And really it’s a love song, its one of the few that Lynyrd Skynyrd’s ever had. This kid was telling me that they used it for their graduation song and not too long ago somebody told me that they used it at a funeral. He said: “For years Skynyrd has always closed the show with that song and the song has different meanings for different people. It peaked at #38 in the Billboard 100 and #48 in Canada.įrontman Johnny Van Zant discussed this song in a track-by-track commentary to promote the band’s 2010 CD/DVD Live From Freedom Hall. In 1976, a live version was released from the One More For the Road live album. The song was released as a single in 1974 and peaked at #19 in the Billboard 100 adn #58 in Canada. Even the band never thought it was going to be a hit. They thought it was too long and that no radio station would play it. ![]() Van Zant finally got inspired one night and had Collins and Gary Rossington play it over and over until he wrote the words.Īt the time of recording, the song was only 7 1/2 minutes long, but throughout the next year, Collins continued to refine the song until it was recorded for the final cut of the Pronounced album in 1973. Collins wrote the music long before Ronnie Van Zant came up with lyrics for it. Guitarist Allen Collins had been working on the song on and off for the previous two years. This song began as a ballad without the guitar solos at the end, and Lynyrd Skynyrd recorded it that way for the first time in 1972. They would soon open up for The Who on their Quadrophenia tour and that helped build their audience. ![]() The album was a very solid album and it peaked at #27 in the Billboard Album Chart, #47 in Canada, and #44 in the UK in 1973. The double guitar solo at the end is the same style as many early Allman Brothers songs.įree Bird was on their debut album Pronounced Leh-nerd Skin-nerd…They gave it the title because well… they knew people would not be able to pronounce their name. The song was written long before his death. The song was usually dedicated to Duane Allman and he died in 1971, two years before “Free Bird” was released. I’ve heard this live before and it is one of the great live songs you can hear. Like the others this week it builds up and it does have an electrifying solo to close it out. There would always be one drunk j ackass person in the back that yelled “Free Bird”…it never failed! I have to admit it was funny the first few times. We didn’t know many Lynyrd Skynyrd songs. When I was playing in clubs and bars we played mostly British rock. There is one more song coming after Free Bird…and we will finish this up. If you need a little help, we have a review program just for you. Determine what didn’t work, make the changes, and move forward without dwelling. If this doesn’t match the image you are trying to portray, then you have a clear path for change. Use this self-reflection to gain a better understanding of how prospective employers see you. This is a great time to reflect on how your resume reads, and how you interacted in failed interviews. Instead of losing heart, we encourage you to take this opportunity to reflect on what you have done in your job search thus far, and what mistakes you may have made. You start out strong and motivated, but after you get turned down over and over, you start to lose steam. We get it – searching for a job can be so discouraging. Through self-reflection, we can start to create a consciousness surrounding our behavior and responses to things, and ideally, make changes to better ourselves. I hate to admit it, but there have been more than a few occasions where I’ve looked back and thought, “man, I really could’ve handled that better.” I think of it like playing back a highlight reel of recent interactions. It is a healthy practice to take inventory of your behavior on a regular basis. No one in their right mind wants to be that person, but sometimes, despite our best efforts, we have moments that reveal just how little self-awareness we have in certain situations. You wonder to yourself, “How can they not see the eye rolls and negative body language around them? Do they not know what this behavior makes everyone think or feel about them?” You know the type – the one who makes people uncomfortable with their off-color jokes, or annoys everyone with their incessant bragging. There is nothing worse than the person at the party with little-to-no self-awareness. ![]() Repeating history will cause you to miss the opportunities waiting just around the corner you haven’t yet traveled down. Holding on to bad habits, guilt, or tired routines prevents us from learning better ways to approach the challenges that life will inevitably throw at us. Holding on to outdated self-perceptions is a really great way to limit yourself from reaching your full potential.Īnother reason why it is so important to let go of the past is that it allows you to make significant life changes. If you’re constantly thinking about the mistakes you’ve made – whether in regards to career moves, personal relationships, or spiritual matters – you may find it hard to shed the old you and embrace the newer, wiser version of yourself. When we’re constantly looking in the past, it’s hard to progress with our goals. Today, we ask you, “Are you living in the rearview mirror?” meaning, are you focusing so hard on your past that you are incapable of moving forward? Reasons to Look Ahead However, we’ve noticed that self-reflection can all too easily turn into an unhealthy dwelling on the past. Self-reflection allows us to observe and analyze how we’ve done in past situations. ![]() Many wise people before us have observed that personal growth requires self-reflection. This month at Vision to Purpose, we’re focusing on personal growth. ![]()
![]() Your homework being eaten does not automatically mean you have a goat. This converse statement is not true, as you can conceive of something … or someone … else eating your homework: your dog, your little brother. Take the first conditional statement from above:Ĭonclusion: … then my homework will be eaten.Ĭonverse: If my homework is eaten, then I have a pet goat. You may "clean up" the two parts for grammar without affecting the logic. ![]() To create a converse statement for a given conditional statement, switch the hypothesis and the conclusion. Whether the conditional statement is true or false does not matter (well, it will eventually), so long as the second part (the conclusion) relates to, and is dependent on, the first part (the hypothesis). If the quadrilateral has four congruent sides and angles, then the quadrilateral is a square.Įach of these conditional statements has a hypothesis ("If …") and a conclusion (" …, then …"). If I ask more questions in class, then I will understand the mathematics better. If I eat lunch, then my mood will improve. If the polygon has only four sides, then the polygon is a quadrilateral. If I have a triangle, then my polygon has only three sides. If I have a pet goat, then my homework will be eaten. In logic, concepts can be conditional, using an if-then statement: Then we will see how these logic tools apply to geometry. To understand biconditional statements, we first need to review conditional and converse statements. One example is a biconditional statement. Geometry and logic cross paths many ways. If we remove the if-then part of a true conditional statement, combine the hypothesis and conclusion, and tuck in a phrase "if and only if," we can create biconditional statements. Both the conditional and converse statements must be true to produce a biconditional statement. We will review the ten postulates that we have learned so far, and add a few more problems dealing with perpendicular lines, planes, and perpendicular bisectors.A biconditional statement combines a conditional statement with its converse statement. Moreover, we will detail the process for coming up with reasons for our conclusions using known postulates. Whenever you see “con” that means you switch! It’s like being a con-artist! In the video below we will look at several harder examples of how to form a proper statement, converse, inverse, and contrapositive. ![]() ExampleĬontinuing with our initial condition, “If today is Wednesday, then yesterday was Tuesday.”īiconditional: “Today is Wednesday if and only if yesterday was Tuesday.” In other words the conditional statement and converse are both true. ExampleĬontrapositive: “If yesterday was not Tuesday, then today is not Wednesday” What is a Biconditional Statement?Ī statement written in “if and only if” form combines a reversible statement and its true converse. Inverse: “If today is not Wednesday, then yesterday was not Tuesday.” What is a Contrapositive?Īnd the contrapositive is formed by interchanging the hypothesis and conclusion and then negating both. So using our current conditional statement, “If today is Wednesday, then yesterday was Tuesday”. Now the inverse of an If-Then statement is found by negating (making negative) both the hypothesis and conclusion of the conditional statement. So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states.Ĭonverse: “If yesterday was Tuesday, then today is Wednesday.” What is the Inverse of a Statement? Hypothesis: “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.” ExampleĬonditional Statement: “If today is Wednesday, then yesterday was Tuesday.” Well, the converse is when we switch or interchange our hypothesis and conclusion. This is why we form the converse, inverse, and contrapositive of our conditional statements. Therefore, we sometimes use Venn Diagrams to visually represent our findings and aid us in creating conditional statements.īut to verify statements are correct, we take a deeper look at our if-then statements. Sometimes a picture helps form our hypothesis or conclusion. In fact, conditional statements are nothing more than “If-Then” statements! To better understand deductive reasoning, we must first learn about conditional statements.Ī conditional statement has two parts: hypothesis ( if) and conclusion ( then). Here we go! What are Conditional Statements? In addition, this lesson will prepare you for deductive reasoning and two column proofs later on. We’re going to walk through several examples to ensure you know what you’re doing. Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher) ![]() This pen can also cover up gel pen and marker ink neatly. Using this pen, you can cover errors on photocopies, computer printouts, and assignments with the utmost ease. The barrel contains 12ml fluid so that you can use it a bit longer than any other white-out pen in the market. But if you want to remove the excess, use a tissue to wipe it out right away. Also, the fluids dry fast and stay longer. This fluid can cover up your mistakes flawlessly leaving a silky smooth finish. The white opaque fluid inside this pen is very high in quality. If you are an artist, then this fine metal tip can help you to create a detailed design or art with this pen. This metal tip makes sure that this pen works smoothly on any rough surface whether it’s metal, glass, or paper.Īlso making sure the fine details while making any correction is another advantage this metal tip provides. The first mind-blowing fact about this pen is its fine point metal tip. Not just me, hundreds and thousands of users have used this pen on multipurpose and they got overwhelmed with its quality. ![]() ![]() Soft squeeze barrels that ensure easy use.ĭo you need a white multipurpose pen that can correct your written mistakes and be used for writing on any dark surface? If yes, then Pentel Presto! Jumbo Correction Pen will be our recommendation.Needlepoint tip for accurate application.It doesn’t matter if you want to use it for your next art project or in your office and home, the top-notch white out will never disappoint you.ĭon't doubt the quality. This BIC Shake ‘N Squeeze Correction Pen can cover tough ink and permanent marker with ultimate smoothness. The rest will be done within no time with the fast-drying fluid of this pen. So your teacher will barely notice the corrections you made in your assignment.ĭo not panic if you have very little time to make all the corrections. Because the bright fluid color blends pretty well with the white paper background. So there will be no waste of fluid.Īnother worth mentioning fact about this pen is its bright fluid that makes the covering area unnoticeable. The soft squeeze barrel of this pen gives you proper control over the amount of fluid release. So to cover up any word from a text will be easier without spreading the fluid all around the correction area. And to make that happen, it has a needlepoint tip to make every stroke precise and thin. Because this pen worth your trust.ĭo you know what is exclusive about this pen? Its accuracy of covering every small detail. ![]() Let this pen make all the corrections you need. Because in this article we are going to introduce to you the top class white out pens available in the market so far.ĭo you need to cover your fine details? BIC White-Out Shake ‘N Squeeze Correction Pen can be a go-to tool for that. It may take your valuable time and much effort. And which pen can you think of more than a white out pen? If you are an artist or designer, the white-out pen can be a perfect addition to your creative collection.īut finding the right one according to your need and expectation can be difficult. But for that, you may require a pen that stands out. Sometimes writing on a dark-colored surface seems fun to so many. With the best white out pen, you can easily make any correction on paper.įorget about corrections. But all those mistakes can be covered by a simple tool- a white-out pen. Wondering which mistakes I am talking about? I am talking about those mistakes you made on paper while writing an important document or maybe filling up an admission form. Yes, we always make mistakes, don’t we? But there are mistakes that we can cover-up. There is a maxim, most probably we all know, that says-Man Is Error”. ![]() ![]() The management team has provided the fund with commendable continuity. An investment of more than$ 1 million would be ideal to align managers' interests with those of the fund's investors. The management team is invested in the fund, but the maximum investment by any manager is between$ 500,000 and$ 1 million. The three listed managers boast 15 years of average portfolio management experience. Shanahan has an experienced backdrop of support. The average Morningstar Rating of the strategies they currently manage is 3.0 stars, reflecting average risk-adjusted performance versus category peers. Shanahan, the longest-tenured manager on the strategy, boasts over 25 years of portfolio management experience. The portfolio's average surveyed credit quality is on par with peers, with both the fund and the average being rated B. Over the past 12 months, the average yield of the fund has been higher than the average yield of its Morningstar Category peers. Higher yields tend to indicate higher credit risk. It also has an 8.3% 30-day SEC yield (a measure similar to yield-to-maturity). This strategy has a 7.2% 12-month yield, higher than its average peer's 7.0%. And finally, the fund leans toward debt with three- to five-year maturities. ![]() Additionally, there's been a notable bias away from junk bonds. Relative to the category average, the managers have beenan overweight corporate debt. Opening the analysis to additional factors, the portfolio has displayed three biases over time, whether towards or away from certain fixed-income instruments. This can be seen in its five-year alpha calculated relative to the category index, which suggests that the process has struggled over that period.Ĭompared with other funds in the Bank Loan Morningstar Category, this fund, historically, hews closely to peers' credit and interest-rate sensitivity. Lastly, the process is limited by the fund's unimpressive long-term risk-adjusted performance. The parent firm's superior risk-adjusted performance, as shown by its average 10-year Morningstar Rating of 3.3 stars, also supports the rating. The measure indicates the percentage of a firm's funds that survived and beat their respective category's median Morningstar Risk-Adjusted Return for the period. The main driver of the rating is the parent firm's five-year risk-adjusted success ratio of 59%. JPMorgan Floating Rate Income Fund earns an Average Process Pillar rating. That shortcut basically moves your files to the new destination. We’re in a pickle here… or are we? You can simply copy the files (command + C), and instead of pasting them, you just press “ command + option + V“. But there is no option to cutfiles in the Finder. While you do have a “control” key on the Mac keyboard, the shortcuts to copy and paste files, folders on a Mac is by using “ command + C“, and “ command + V“, respectively. Now that you’re about to copy your files into the work folder that you created, maybe you realised you actually want to move them there. Pay heed to Applications, this is where all of your applications are.Ĭopying and pasting files on a Mac works just as it does on Windows… almost. The most common places you need to know about, are all available in your Finder sidebar. To teach by analogy, it’s as if there was only a C: drive on your PC, and all your files were stored in there. If you haven’t, don’t worry, it’s not too hard to figure out. If you’ve ever used a Linux machine, you’ll be right at home with the macOS way of handling files. Instead, macOS treats your entire drive as one drive, and creates a single tree of destinations on it. Macs don’t organise files the way Windows does, and you will not see any drive partitions like “C, D, E, etc”. While you’re still in the Finder, you should probably get acquainted with the way your files are managed by macOS. Get Information (Properties) about a File or Folder: command + I.That’s right, the Finder supports tabbed browsing. Believe me, you’ll love it. Note : You can actually use “command + W” in any app, actually, and it is extremely handy while closing tabs in a browser, or in the Finder. You can also use the shortcut “ command + W” to close the window. You’ll see that it reveals an “X” mark as soon as your cursor hovers over it. ![]() You can click on this icon to safely remove the drive from your Mac, before disconnecting it.Ĭlosing the Finder window is easy, as well – just click on the red button on the top left corner. If you have connected a USB drive, or an external hard disk to your Mac, they will appear on the Finder side-bar as well, along with an eject icon next to their names. This is the Mac equivalent of the “Windows Explorer”, and this is where you’ll manage your files, create folders, smart folders, add tags, and basically do everything related to file management. Click on it, and you’ll see a “ Finder Window” open up for you. You can see the dots in the screenshot, under the icons for Finder, Chrome, and Quip. ![]() For a $1.99 investment, this app provides more than enough functionality to make it well worth it.Before you start wondering where the “Explorer” has gone off to, let me tell you that a Mac uses what Apple calls a “Finder”, and it is always open… waiting to help you manage your files. On the “Dock” (that’s the thing on the bottom of the screen), you’ll notice a few (a lot of) standard things that you might want to get started with. All open apps have a small black dot below their icon in the dock, just to help you identify the apps that are currently open. You can tailor its functions to suit your specific needs, and the only major drawback is that there is little help to be found if you do need it. Bottom LineīetterSnapTool works well and provides a convenient service for helping to keep your screen clear and organized as you work. While the app does work well, there seems to be nothing you can do if you run into a problem, which is unusual for a paid program. No help: There is no Help feature to go along with this program, and there is also not much in the way of support. You can set a particular size and shape for a window, and then you can assign it a command or hot key for quick access whenever you need it. Depending on where you drag the window, it will react in a different way, and the interface descriptions make it easy to see what will happen in different cases, so you can get the result you want.Ĭustomizations and shortcuts: In addition to the standard set of window sizes and shapes that come preset with the program, you also have the option of creating your own. Smooth functionality: This app works just as advertised, and when you snap it against the edge of the screen it will immediately resize to preset parameters. You can snap them against the sides or the corners, and you can even set custom window sizes and placements for certain specific situations. BetterSnapTool for Mac is a handy utility that lets you automatically resize windows by dragging them to different areas of the screen. ![]() But this isn't our case, We provide you an easy-to-use online tool that has been tested many times. ![]() Software apps often have a poor reputation for being plagued with phishing and malware threats over time. Our service is 100% safe to download any video without viruses. Fully compatible and supported by all browsers. You can download many YouTube videos as much as you want. ![]() YouTube4KDownloader offers an easy tool to cut any YouTube video at your specified time frame and download at many formats and qualities. easily and fast using our service YouTube4KDownloaderĮasily download any YouTube private or restricted video in FHD formats using YouTube Private Downloader.Įasily download YouTube video subtitles in many formats like SRT, VTT, TXT, and DFXP with more than 100 different languages to choose from. 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If you own too much watches date makes the life much more complicated, haha. I also quite like that they made it a no-date version, it just makes the dial cleaner and it is a plus for me as I don’t like date feature that much. At 6 o’clock we have writing like the name of the watch “Sea Star” and the depth rating “1000ft/300m”. At 12 o’clock we have ” Aquatico” brand name with “ Automatic” written under the brand name which in my opinion is unnecessary detail + it kind of cheapens the watch. The red second’s hand nicely accents the dial and I like that arrow shape it has. ![]() The sword hour and minute hands are also made of brass. The hour markers are made of brass btw and in my opinion they look pretty cool, gives the watch that gilt dial vibe. Around the dial we have a minute track printed in white and applied hour markers with lume in the middle of them. The dial is blue and it really pops because of the sapphire crystal that is domed from the underside. The water resistance is 300m (30ATM) which more than enough to swim with the watch without a problem! On top of the watch, we have boxed sapphire crystal with dome from the inside and AR coating on the underside. The exhibition screw-in stainless steel case back has a flat sapphire crystal with specifications engraved around the edge. The crown action is pretty good! The one thing I don’t like about the new version is that they removed the drilled lugs, which made changing strap easier, at least for me. At 3 o’clock we have a screw-down crown which is signed on top. Bezel has no play, the clicks are precise and it works really good! The ceramic bezel insert is pretty good and I like that red triangle at 12 o’clock and all markers on the insert are lumed with Superluminova BG W9 which glows in this blueish colour. The uni-directional 120 click bezel is pretty good for a watch at this price, sometimes even better than much more expensive pieces from other brands. The case diameter is 42mm, the thickness is 14mm and from top to bottom the case measures at 49,5mm. The case is finished in the satin-brushed finish, which is really well done, the edge of the bezel has a bit of polished finishing! I wish they added more polished edges on the lugs or any other details as then the watch would look a ton better. The case is very well machined actually, a bit better than the bronze version that I have had for review. The case of the Sea Star is made of 316L stainless steel. And the best part? It costs just 299$ which is probably the best price for a dive watch out there in microbrand market, of course, other choices may be beeing Phoibos! The watch was very neatly boxed in a nice square box signed by Aquatico. The case looks really sharp, the ceramic insert is nice! The bezel has a very nice action to it! Plus it comes with an extra blue nato strap, maybe not the best, but it is there. When the watch arrived I was actually surprised how good it looked in real life. There are many colour, dial and hand options and two movement options as previously mentioned. Although I don’t see paying 200$ more for a Sellita as it isn’t the best Swiss movement and ETA 2824 would be a lot better, but with current situation with ETA suplliers it is almost impossible to get if watches aren’t made in Switzerland, thus making them a lot more expensive.Īnycase, the version that Aquatico chose to send me is the Sea Star with a blue dial and bezel insert and with NH35 movement. What I like about the new versions is that they include a version with a Seiko NH35 movement for 299$ and for 499$ you can get the same watch with Sellita SW200. Sea Star collection which is a dive watch inspired by the Tudor Black Bay watches. ![]() Today we are looking at the version 2.0 of the Sea Star in stainless steel. Today we are looking at a brand that has been featured on my blog a couple of times and we even have reviewed the same version of the watch in bronze and with different dial layout and colour. |
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