Inside of a rubik - Inside Rubik’s Cube and Beyond. On January 30, 1975 Ernd Rubik j r., professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"--A game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube ...

 
Feb 12, 2022 · This Rubik's cube is the easiest and the hardest at the same time. It's 1x1 and the fun part about it is that it's always in the solved state. It seems prett... . Maryland women

For today's challenge, I am going to solve a 3x3x3 Rubik's cube that is missing one of the corner pieces!Buy SpeedCubes here: http://www.speedcubeshop.com?rf... Inside Rubik's cube and beyond. 1982, Birkhäuser. in English. 3764330783 9783764330781. aaaa. Not in Library. Libraries near you: WorldCat. Add another edition?Mar 24, 2023 · THE ORIGINAL RUBIK’S CUBE: A combination of mathematics, art and science - the iconic Rubik’s Cube challenges your mind and problem-solving skills. The classic 3x3 Rubik’s Cube is the world’s best-known addictive puzzle and has fascinated fans since its launch in 1980. 3. This will be our model cube (just so we're all on the same page of the face (center block) colors) -. I've been trying to work on this, but I don't know enough math to formulate a rule. But, given the pattern -. A B B A B B A C C. We can note that each block of 4 that match in the upper right, it has 3 matches to its left (depending on which ...C. Bandelow. On January 30, 1975 Ernd Rubik j r. , professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France ...# Inside the Rubik's Cube What is inside the rubik's cube? It starts with an imagination of a space that rotates around regarding gravity. Where do we stand? Why do we have to stand on the same side? I think every combination is each a unique answer. So, be one of the answers! We are all all right :DPut in the edges around the equator of the cube. For the last 3rd put the remaining pieces in except one edge. REMEMBER, edge pieces go in easiest when the layer is turned 45 degrees. To put the final edge in turn the layer 45 degrees and wedge one side under the center piece. Then press down and inward towards the center of the cube.THE ORIGINAL RUBIK’S CUBE: A combination of mathematics, art and science - the iconic Rubik’s Cube challenges your mind and problem-solving skills. The classic 3x3 Rubik’s Cube is the world’s best-known addictive puzzle and has fascinated fans since its launch in 1980.Anything can be done if you focus really hard! In this time-lapse, I solve a 21x21x21 Rubik's Cube! My next goal will be the 31x31x31. If this video gains tr...The 1x1x1 cube is a cube that is always in the solved state. It cannot be turned in any way because it is only one little cubie. The cube's only purposes are for fun and collecting, although some people will correctly say that it is the hardest cube to solve. The current unofficial World Record for the 1x1x1 Rubik's Cube is 0.001 seconds by both Kewbix and Mr Cube. The cube is made from a ... Another book on Rubik's cube? Yes, but for ardent cubemeisters and all those who are interested in the mathematics of the cube, it was very much worth doing. It is a splendid book, clearly written, enlivened by delightful cartoons, and containing a wealth of informa­ tion not to be found in any other book." -MARTIN GARDNERhow to make a cube in a cube in a cube on the rubiks cubeThis is a very easy Cue in a cube in a cube pattern. Rubiks cube patterns are very easy and fun to m...Sep 1, 2023 · WHAT IS INSIDE RUBIK CUBEYour queries-cuberubiks cuberubik's cubewhat is inside rubik's cubewhat is inside speed cuberubix cuberubikrubic cuberubixwhat's ins... The patent approval finally came in early 1977 and the first Cubes appeared at the end of 1977. By this time, Erno Rubik was married. Two other people applied for similar patents at about the same time as Rubik. Terutoshi Ishige applied a year after Rubik, for a Japanese patent on a very similar cube. An American, Larry Nichols, patented a cube ...Mar 12, 2019 · The patent approval finally came in early 1977 and the first Cubes appeared at the end of 1977. By this time, Erno Rubik was married. Two other people applied for similar patents at about the same time as Rubik. Terutoshi Ishige applied a year after Rubik, for a Japanese patent on a very similar cube. An American, Larry Nichols, patented a cube ... Douglas Hofstadter wrote an excellent introduction to the Rubik’s cube in the March 1981 issue of Scienti c American. There are several books about the Rubik’s cube; my favorite is Inside Rubik’s Cube and Beyond by Christoph Bandelow. David Singmaster, who developed much of the usual notation for the Rubik’s cube, REDDIT https://www.reddit.com/r/dopeornopesubmissionsHigh Steaks https://www.youtube.com/watch?v=_ZUr3kaz5wIIT'S PUZZLE TIME. Today we are looking throug...How To: Solve a Rubik's Cube for dummies How To: Solve a Rubik's Cube with famous speedcuber Tyson Mao How To: Solve a Rubik's Cube blindfolded & in five easy steps How To: Solve the Rubik's Cube F2L with the Fridrich Method7.1K views 5 years ago. What is inside of a 3x3 Rubik's Cube? Have you ever wonder what's the famous Rubik's Cube looks like on the inside? By Crazy Russian Official Show more.Feb 24, 2021 · February 24, 2021 9:52am. Netflix. Sue Kim, director of an Oscar-shortlisted short documentary about competitive Rubik’s Cubers, can solve a complex storytelling puzzle in under 40 minutes. In ... The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. Generally speaking, uppercase letters ( F B U D L R) refer to the outermost portions of the cube (called faces). Lowercase letters ( f b u d l r) refer to the inner portions of the cube (called slices).Jun 23, 2022 · Use code TINGMAN for a discount off every order at Daily Puzzles!http://dailypuzzles.com.au/tingmanAlgorithm: U’ L’ U’ F’ R2 B’ R F U B2 U B’ L U’ F U R ... Inside Rubik’s Cube and Beyond Authors: Christoph Bandelow 0; Christoph Bandelow. Bochum-Stiepel, Federal Republic of Germany. View author publications ...Inside Rubik’s Cube and Beyond Authors: Christoph Bandelow 0; Christoph Bandelow. Bochum-Stiepel, Federal Republic of Germany. View author publications ...Jul 22, 2023 · Solving the First Layer. 1. Choose a face. As a beginner, choosing to begin with the yellow-colored face is most common and highly recommended. Although you can solve the Pyraminx by starting with any color, yellow is highly recommended as it is similar to the white face of the Rubik's cube. Okay. Might just be dust, but probably silicone spray residue. Yes, you can clean it if you want. It is ground plastic dust. This is common especially with new or unlubricated cubes. Take it part and wash the pieces in soapy water, lube and reassemble. It will be a lot smoother.Douglas Hofstadter wrote an excellent introduction to the Rubik’s cube in the March 1981 issue of Scienti c American. There are several books about the Rubik’s cube; my favorite is Inside Rubik’s Cube and Beyond by Christoph Bandelow. David Singmaster, who developed much of the usual notation for the Rubik’s cube, This is a tutorial on how to solve a Rubik’s cube inside a paper bag. It is a magic trick with a real cube that you might have seen performed on TV.Buy a sp...Feb 12, 2022 · This Rubik's cube is the easiest and the hardest at the same time. It's 1x1 and the fun part about it is that it's always in the solved state. It seems prett... We cut open, smashed open and pulled open 4 different Rubik’s Cubes to see what they are made of! This was really fun and interesting. Thank you to our many ... See full list on popularmechanics.com THE ORIGINAL RUBIK’S CUBE: A combination of mathematics, art and science - the iconic Rubik’s Cube challenges your mind and problem-solving skills. The classic 3x3 Rubik’s Cube is the world’s best-known addictive puzzle and has fascinated fans since its launch in 1980.On January 30, 1975 Ernd Rubik j r., professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France and the Magic Cube ...Jun 23, 2022 · Use code TINGMAN for a discount off every order at Daily Puzzles!http://dailypuzzles.com.au/tingmanAlgorithm: U’ L’ U’ F’ R2 B’ R F U B2 U B’ L U’ F U R ... The movie shows him downloading files onto an SD card and then hiding it inside a Rubik’s cube. He then avoids running the Rubik’s cube through security by tossing it to a security guard, who ...Update: New and improved version. Faster, better, and supports more devices. Solving the Rubik's Mini Cube (2x2x2) may sometimes seem like an easy task comparing to solving its predecessor the original Rubik's Cube (3x3x3), however it can still pose a decent challenge for most of us - especially when trying to solve it in the shortest possible way.Aug 9, 2020 · how to make a cube in a cube in a cube on the rubiks cubeThis is a very easy Cue in a cube in a cube pattern. Rubiks cube patterns are very easy and fun to m... Apply the inverse rotations of the backward algorithm to revert the cube to the solved cube (or the initial position). Let's take a short algorithm for the demonstration, the Cross: U F B’ L2 U2 L2 F’ B U2 L2 U. Written backwards: U L2 U2 B F’ L2 U2 L2 B’ F U. Replace the moves with the inverse rotations: U’ L2 U2 B’ F L2 U2 L2 B F ...See full list on popularmechanics.com Okay. Might just be dust, but probably silicone spray residue. Yes, you can clean it if you want. It is ground plastic dust. This is common especially with new or unlubricated cubes. Take it part and wash the pieces in soapy water, lube and reassemble. It will be a lot smoother.# Inside the Rubik's Cube What is inside the rubik's cube? It starts with an imagination of a space that rotates around regarding gravity. Where do we stand? Why do we have to stand on the same side? I think every combination is each a unique answer. So, be one of the answers! We are all all right :DThis video tutorial will teach you how to disassemble and reassemble 2x2 Rubik's Cube puzzles. See the process of the 2x2 Rubiks Cube disassembly and reassembly, which is very handy for the ever-necessary lubing (especially for speedsolving), curiosity and cheating (cheating is not recommended). There are three different 2x2 puzzles that you ...An explanation to the workings and layout of a 3x3x3 Rubik's cubeThe Rubik’s Cube was invented in 1974 by Ernõ Rubik, a Hungarian architecture professor. Rubik later used the Cube as a learning exercise to teach his students about 3-dimensional spaces. Little did he know his “Magic Cube” (as he originally named it) would become one of world’s most famous puzzles of all time!Sep 2, 2022 · But of course I can't forget about Rubik's. Back in July, I wrote about Rubik's opening up a new location on the east side. For a long while the only one in town was located on Mesa on the west side. After months of teasing & waiting, the wait is finally over as they opened up their 2nd location this weekend: Located at 9910 Montana. 1. Familiarize yourself with the Rubik's Cube. Recognize where each of the colors lie on the completed cube. [1] Notice (going clockwise) the Red, White, and Blue faces of the cube are on one side and the Green, Orange, and Yellow faces are on another. This is the standard setup for newer, standard cubes.The Rubik’s Cube was invented in 1974 by Ernõ Rubik, a Hungarian architecture professor. Rubik later used the Cube as a learning exercise to teach his students about 3-dimensional spaces. Little did he know his “Magic Cube” (as he originally named it) would become one of world’s most famous puzzles of all time!Bounds on Solving a Rubik’s Cube The number of possible permutations of the squares on a Rubik’s cube seems daunting. There are 8 corner pieces that can be arranged in 8! ways, each of which can be arranged in 3 orientations, giving 38 possibilities for each permutation of the corner pieces. There are 12 edge pieces which can be arranged in ...C. Bandelow. On January 30, 1975 Ernd Rubik j r. , professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France ... The Rubik’s cube is manufactured by melting and molding together plastic pellets to form the components and the structure of the cube. The parts are then inspected by hand to ensure they were formed properly. From there the Rubik’s cube components enter into an assembly line where the construction process is completed, the cubelet stickers ...Online Rubik's Cube, 4x4x4 and other NxNxN cube solver and simulator. Set up a scramble to find the rotations leading to the solutionUse code TINGMAN for a discount off every order at Daily Puzzles!http://dailypuzzles.com.au/tingmanAlgorithm: U’ L’ U’ F’ R2 B’ R F U B2 U B’ L U’ F U R ...We cut open, smashed open and pulled open 4 different Rubik’s Cubes to see what they are made of! This was really fun and interesting. Thank you to our many ...The 1x1x1 cube is a cube that is always in the solved state. It cannot be turned in any way because it is only one little cubie. The cube's only purposes are for fun and collecting, although some people will correctly say that it is the hardest cube to solve. The current unofficial World Record for the 1x1x1 Rubik's Cube is 0.001 seconds by both Kewbix and Mr Cube. The cube is made from a ... Jul 18, 2020 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ... The Rubik's Cube (3x3x3) is a cube shaped Twisty puzzle. It was invented in 1974 by a Hungarian professor named Ernő Rubik. Rubik originally name the puzzle "Magic Cube" however, in 1980 it was renamed after its creator and is generally known since as the "Rubik's Cube". During the 1980s, the Rubik's Cube became a worldwide sensation, and it ...Shawn Farquhar, two-time world champion of magic and two-time Penn & Teller Fool us winner, teaches you how to make your own impossible bottle with a Rubik's...THE ORIGINAL RUBIK’S CUBE: A combination of mathematics, art and science - the iconic Rubik’s Cube challenges your mind and problem-solving skills. The classic 3x3 Rubik’s Cube is the world’s best-known addictive puzzle and has fascinated fans since its launch in 1980.Erno Rubik, who devised one of the world’s most popular and enduring puzzles, opens up about his creation in his new book, “Cubed.”. 140. Erno Rubik, who invented the Rubik’s Cube, wrote ...The Rubik's Cube (3x3x3) is a cube shaped Twisty puzzle. It was invented in 1974 by a Hungarian professor named Ernő Rubik. Rubik originally name the puzzle "Magic Cube" however, in 1980 it was renamed after its creator and is generally known since as the "Rubik's Cube". During the 1980s, the Rubik's Cube became a worldwide sensation, and it ...Jul 13, 2020 · The Mathematical Mystery Behind Rubik’s Cube. Forty-three quintillion. Or more precisely, 43,252,003,274,489,856,000. This impressive figure is the number of tile combinations possible in the Rubik’s Cube (also known as the Magic Cube), the most famous puzzle of all times. Bearing this data point in mind, it is not surprising that the goal ... Inside Rubik's cube and beyond. 1982, Birkhäuser. in English. 3764330783 9783764330781. aaaa. Not in Library. Libraries near you: WorldCat. Add another edition?A Rubik’s Cube has one core, eight corner cubies, and 12 edge cubies. The immediate math to be done with those numbers is the total number of ways you can scramble a Rubik’s cube: 43,252,003,274,489,856,000. Written in a more mathematical way, that number is (3 8 8!) (2 12 12!)/12. Here’s how that comes together.Sep 2, 2022 · But of course I can't forget about Rubik's. Back in July, I wrote about Rubik's opening up a new location on the east side. For a long while the only one in town was located on Mesa on the west side. After months of teasing & waiting, the wait is finally over as they opened up their 2nd location this weekend: Located at 9910 Montana. Douglas Hofstadter wrote an excellent introduction to the Rubik’s cube in the March 1981 issue of Scienti c American. There are several books about the Rubik’s cube; my favorite is Inside Rubik’s Cube and Beyond by Christoph Bandelow. David Singmaster, who developed much of the usual notation for the Rubik’s cube, The old design is durable, cost efficient and easy to disassemble. Also, it makes the mediocrity of the Rubik's brand cube even more inexcusable because this is not even the original design. Either stick with the simple design from the 1980s or redesign it to be a good speed cube, instead of redesigning the core for no reason.Inside Rubik's Cube And Beyond| C Bandelow. I Choose You 2. Learning outcomes. 1 of 5 stars 2 of 5 stars 3 of 5 stars 4 of 5 stars 5 of 5 stars. Be a mother to my children. The Nervous Housewife. By Shore and Sedge. Shared By Two (Seeding Eden 2) by Aya Morningstar.REDDIT https://www.reddit.com/r/dopeornopesubmissionsHigh Steaks https://www.youtube.com/watch?v=_ZUr3kaz5wIIT'S PUZZLE TIME. Today we are looking throug...Apply the inverse rotations of the backward algorithm to revert the cube to the solved cube (or the initial position). Let's take a short algorithm for the demonstration, the Cross: U F B’ L2 U2 L2 F’ B U2 L2 U. Written backwards: U L2 U2 B F’ L2 U2 L2 B’ F U. Replace the moves with the inverse rotations: U’ L2 U2 B’ F L2 U2 L2 B F ...Nov 6, 2022 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ... On January 30, 1975 Ernd Rubik j r., professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France and the Magic Cube ...Apr 1, 2021 · Learning to solve a Rubik's Cube can be easy!Where I get my cubes:1x1 https://speedcubeshop.com/products/1x1-speed-cube3x3 https://speedcubeshop.com/prod... ture inside is the key to the Rubik ... Solving Rubiks Cube Using Open CV. Article. Jun 2022; Sudhan M.B; The Rubik’s cube is 3D combinatorial and mechanical puzzle invented in 1974. It ...Cube in this video: https://amzn.to/348F9U7This video tutorial shows how to make a Cube in a Cube in a Cube patternCheck out more at https://www.youtube.com/...C. Bandelow. On January 30, 1975 Ernd Rubik j r. , professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France ... Inside Rubik's cube and beyond. 1982, Birkhäuser. in English. 3764330783 9783764330781. aaaa. Not in Library. Libraries near you: WorldCat. Add another edition?how to make a cube in a cube in a cube on the rubiks cubeThis is a very easy Cue in a cube in a cube pattern. Rubiks cube patterns are very easy and fun to m...Rubik's Cube Algorithms. A Rubik's Cube algorithm is an operation on the puzzle which reorients its pieces in a certain way. Mathematically the Rubik's Cube is a permutation group: an ordered list, with 54 fields with 6*9 values (colours) on which we can apply operations (basic face rotations, cube turns and the combinations of these) which reorient the permutation group according to a pattern.From GAN13 onFull Magnet Force. The first GAN cube to completely fill its internal space with 88 magnets. The performance of ECP 3.0 will outperform the single-line magnetic positioning systems. 8 Core Magnets. 12 Repulsion Magnets. 56 Attraction Magnets. 12 Repulsion Rings. Enhanced Core Positioning 3.0.Sep 2, 2020 · Shop our Rubik's MINI 2x2 range here:UK: https://bit.ly/2F62mLQEU: https://bit.ly/3lP8zgiUSA: https://bit.ly/2F0UcVrBe a solver of tomorrow and check out our... # Inside the Rubik's Cube What is inside the rubik's cube? It starts with an imagination of a space that rotates around regarding gravity. Where do we stand? Why do we have to stand on the same side? I think every combination is each a unique answer. So, be one of the answers! We are all all right :D Dec 29, 2020 · 4. 13x13 Power Speed Cube Puzzle. Creators have strived to develop new and harder twisty puzzles as a version of the original Rubik’s Cube. The most common type of the Rubik’s Cube is like the 3x3 but bigger. They can be 13x13 or N x N, also known as ‘Reduction’ or ‘Redux’. The Rubik’s Cube was invented in 1974 by Ernõ Rubik, a Hungarian architecture professor. Rubik later used the Cube as a learning exercise to teach his students about 3-dimensional spaces. Little did he know his “Magic Cube” (as he originally named it) would become one of world’s most famous puzzles of all time!

On January 30, 1975 Ernd Rubik j r., professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France and the Magic Cube .... Platinum gentleman

inside of a rubik

Nov 6, 2022 · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright ... We cut open, smashed open and pulled open 4 different Rubik’s Cubes to see what they are made of! This was really fun and interesting. Thank you to our many ...Aug 26, 2015 · 3. This will be our model cube (just so we're all on the same page of the face (center block) colors) -. I've been trying to work on this, but I don't know enough math to formulate a rule. But, given the pattern -. A B B A B B A C C. We can note that each block of 4 that match in the upper right, it has 3 matches to its left (depending on which ... The 4×4×4 and larger cubes use an extended notation to refer to the additional middle layers. Generally speaking, uppercase letters ( F B U D L R) refer to the outermost portions of the cube (called faces). Lowercase letters ( f b u d l r) refer to the inner portions of the cube (called slices).The Rubik’s Cube was invented in 1974 by Ernõ Rubik, a Hungarian architecture professor. Rubik later used the Cube as a learning exercise to teach his students about 3-dimensional spaces. Little did he know his “Magic Cube” (as he originally named it) would become one of world’s most famous puzzles of all time! 1 year later and I am back (again, again)More alcohol. More Rubik's Cubes.Leave some questions for Episode 4's Q&A!I'm thinking of live streaming on Twitch s...Erno Rubik, who devised one of the world’s most popular and enduring puzzles, opens up about his creation in his new book, “Cubed.”. 140. Erno Rubik, who invented the Rubik’s Cube, wrote ...Cube in this video: https://amzn.to/348F9U7This video tutorial shows how to make a Cube in a Cube in a Cube patternCheck out more at https://www.youtube.com/...Apply the inverse rotations of the backward algorithm to revert the cube to the solved cube (or the initial position). Let's take a short algorithm for the demonstration, the Cross: U F B’ L2 U2 L2 F’ B U2 L2 U. Written backwards: U L2 U2 B F’ L2 U2 L2 B’ F U. Replace the moves with the inverse rotations: U’ L2 U2 B’ F L2 U2 L2 B F ...This is a tutorial on how to solve a Rubik’s cube inside a paper bag. It is a magic trick with a real cube that you might have seen performed on TV.Buy a sp...C. Bandelow. On January 30, 1975 Ernd Rubik j r. , professor of architecture and design in Budapest, was granted the Hungarian patent number 170062 for a "terbeli logikai jatek"-a game of spatial logic. Between 1978 and March 1981 this object-Bt1vos Kocka in Hungary, der Magische Wiirfel or Zauberwiirfel in Germany, Ie Cube Hongrois in France ... Inside Rubik's cube and beyond. 1982, Birkhäuser. in English. 3764330783 9783764330781. aaaa. Not in Library. Libraries near you: WorldCat. Add another edition?Ever wonder what a Rubik's Cube looks like on the inside? In this video we'll take an in-depth look to see how the pieces fit together. Get your Rubik's cube here: https://goo.gl/BEo1W5 Made with Blender 2.73 Music: "Plain Truth" by Gunar Olsen (youtube audio library) #rubiks #rubikscube #b3dSep 1, 2023 · WHAT IS INSIDE RUBIK CUBEYour queries-cuberubiks cuberubik's cubewhat is inside rubik's cubewhat is inside speed cuberubix cuberubikrubic cuberubixwhat's ins... For today's challenge, I am going to solve a 3x3x3 Rubik's cube that is missing one of the corner pieces!Buy SpeedCubes here: http://www.speedcubeshop.com?rf....

Popular Topics