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## Blog Posts (23)

- The Number of Lattice Squares*
There are many puzzles about the number squares you can draw by using the grid points ( lattice points) on a given grid. Here is an example; The correct answer is not 9 (the number of 1x1 squares). There are many other squares you can create using the given points. These hard to catch tilted squares makes these puzzles interesting! Now we have a harder puzzle to work on! What is the total number of squares that can fit into an n x n grid? *Lattice squares are the squares whose vertices are on the grid points. There are two types of lattice squares, grid ones and the tilted ones. Let’s define a "grid square" as a square whose vertices are lattice points and sides are along the axis. (vertical squares). They are easy to create and have square number areas. A "tilted square" is a square whose vertices are still lattice points, but its sides are not along the axis. Tilted squares have whole number areas. The side length of a tilted square can easily be found by using the Pythagorean Theorem. Now, let’s have a look at a 3 x 3 squares and find the total number of grid and tilted squares that can be drawn using the lattice points. The number of grid squares that can be drawn is 9 +4 +1 = 14 Now, let’s find the number of tilted squares The number of tilted squares that can be drawn is 4 + 2 = 6. Then, the total number of lattice squares is 14 + 6 = 20 by using the points of a 3 x 3 grid. One may wonder if there is a short way of finding the number of squares for an n x n square. The questions we need to answer are; The number of grid squares in a n x n square The side length of the biggest tilted square that can be drawn in an n x n square The number of tilted squares in a n x n square The total number of lattice squares in an n x n square. Any relation among the number of tilted squares and grid squares We need to investigate all the possible squares carefully and record our findings systematically to be able to find answers to these questions. Here is a Polypad file you can work on to make drawings; You may need more grids to highlight to create different squares. Good luck! ------ ***------ SOLUTION We can start solving this puzzle by remembering another one! Famous" Checkerboard Puzzle". The answer of the Checkerboard Problem gives us the number of grid squares. To be able to find the total number of squares on a checkerboard, we need to consider that the board has 2 x 2 squares, 3 x 3 squares, 4 x 4 squares and so on other than 64 unit squares. If we organize our findings in a table. We may easily see that they follow the pattern of square numbers. Number of Grid squares in a n x n square; So for an n x n grid, the number of normal grid squares is simply the sum of the square numbers. One way to express the number of grid squares in an n x n grid is; When it comes to find the number of the tilted squares, we may discover different patterns. If you need an extra help for finding the side lengths of the tilted squares, you may have a look at the Square Areas on Grid Polypad Activity. When we organize the data for the tilted squares, one particular pattern can catch your eye. The number of √2 x √2 squares also follows the pattern of square numbers and so does 2√2 x 2√2 and 3√2 x 3√2 … The other tilted squares with the side lengths √5, √10, √13 … can be tricky to count. Be aware the symmetry of the square can make a different square now! √5 x √5 Example in a 4 x 4 grid square; There are 8 of them. If we have a closer look to 4 x 4 grid square, we see that there are 20 tilted square and 30 grid squares. Now, let’s have a look at the 5x5 case; Now there are 50 tilted squares and 55 grid squares. If you repeat the same steps for a 6 x 6 grid; We see that there are 105 tilted squares. You may realize that; In a n x n grid, the total number of grid squares and tilted squares, is equal to the number of tilted squares in a (n+1)×(n+1) grid. Now, let’s try to figure out the side length of the biggest tilted square that can fit into an n x n grid. Let “c” be the side length of the tilted square in a grid. By Pythagorean theorem a^2+b^2=c^2 and we also know that a+b can be at most n units long. a+b <= n For example in a 5 x 5 grid; you may draw “a+b” can never exceed the value of n. Let’s now try to write the side lengths of the tilted squares which will be added to the list for an 7x 7 grid. Find a + b <=7 the new values will be 6 +1 , 5+2 and 4+3 Now, let’s organize our findings about the tilted squares for each n x n grid; Here you may want to double check your results by comparing the patterns you have discovered before. Try to write the new values for 7x7 One way to express the number of tilted squares in a n x n square So the total number of lattice squares in a n x n grid can be found by These expressions can also prove our previous discovery about the total number of lattice squares in a n x n grid, the number of tilted squares in a (n+1)×(n+1) grid. One of the best outcomes of working on a problem like this is the beauty of the solution! Extension: Can we derive a formula for the total number of lattice squares in an n x m rectangular grid where n>m?

- Atatürk ve Matematik
10 Kasım Atatürk'ü anlamak için sadece savaş alanındaki dehasını yada devlet yaratma ve biçimlendirme becerisini konuşmak, okumak yetmez. Onun bilime ve eğitime verdiği değeri ve ülkemizin yeni nesillerinden beklentilerini anlamak da çok önemli. Bunu yaparken onun düşüncelerini ve fikirleri oluşturan deneyimlerini ve araştırmalarını, modern Türkiye'yi kurma amacıyla hangi kaynaklardan yararlandığını bilmek ve bu kaynaklara ulaşabilmek, onu anlamak yolunda ilk adım olabilir. Atatürk'ün hayatı boyunca 4000 kitaptan fazlasını okuduğunu biliyoruz. Atatürk'ün okuduğu kitapların, 1741'inin Çankaya Köşkü, 2151'nin Anıtkabir, 102'sinin İstanbul Üniversitesi Kütüphanesi ve 3'ünün ise Samsun İl Halk Kütüphanesi'nde olduğu biliniyor. Sadi Borak tarafından yazılan kısa metinde, Atatürk'ün bu kitapları okurken aldığı notlar şu şekilde açıklanmış; Bu 10 Kasım'da, O'nun fikirlerinin temellerini oluşturan kitaplara bir göz atalım. Bu kitapları okumak, onu anlamak yolunda, başkalarının fikirlerini dinlemek yerine atabileceğimiz en somut adım olacaktır. Aşağıdaki interaktif Google sınıfını buradan indirip, linklere ve videolara ulaşabilirsiniz. 23 Nisan Yakında .. 19 Mayıs Yakında .. 29 Ekim Yakında ..

- Flextangles
Flextangles are paper models with hidden faces. They were originally created by the mathematician "Arthur Stone" in 1939 and became famous when Martin Gardner published them in December 1956 issue of The Scientific American. Although you can find many different examples and ready to use templates on the web, the best method is to create your own template by using an interactive geometry software like GeoGebra. As a class activity creating flextangles by using a software can lead to discussions about translation and reflection. Flextangles, gizli yüzleri ortaya çıkarmak için esnetilebilen kağıt modellerdir. İlk olarak 1939'da Matematikçi Arthur Stone tarafından yaratılan flextangles, Martin Gardner'ın 1956 Aralık ayında The Scientific American'da yayınladığı makalede yeralınca, ünlü hale geldi. Webde bir çok örneğini ve taslak çizimlerini bulabileceğiniz flextangles için, GeoGebra gibi herhangi gibi geometri programı kullanarak kendi tasarımlarınızı da yaratabilirsiniz. Flextangle ları bir sınıf aktivitesi olarak program yardımıyla tasarladığınızda öteleme ve yansıma konularında da pratik sağlıyor. Ready to use Templates / Kullanıma Hazır Taslaklar: ------ ------ ------

## Other Pages (42)

- Pi Day | MATH FAN
Pi Day is celebrated on the 14th of March (3.14) around the world. Now it is also International Day of Mathematics. That's a fact that the Pi is the iconic number of mathematics, so there are plenty of websites & blogs, and zillions of activities out there to celebrate this day. Here are some of my favorite activities I have used with the Middle School and Elementary School Students; Classroom Posters Free Download Fun Facts About Pi Free Download Calculating Pi Like Archimedes Free Download Pi Day Free Download Can't Stop Free Download Iconic Number Free Download Inspire! UNESCO announced Pi-Day as the International Day of Mathematics in 2019. "Greater global awareness of mathematical sciences is vital to addressing challenges in areas such as artificial intelligence, climate change, energy, and sustainable development, and to improving the quality of life in both the developed and the developing worlds." Do not forget to check out the International Day of Mathematics Page for the posters! 2020 - Mathematics is Everywhere. (The first-ever International Day of Mathematics) 2021 - Mathematics for a Better World . 2022 - Mathematics Unites. Circles and Pi Course Best - Free - Online Interactive Pi Content First Pi Day Celebration in History A recipe for beating the record of most-calculated digits of pi Akira Haraguchi, 69, memorises π to 111,700 digits. Memorizing Pi How many decimals of pi (π) NASA-JPL scientists and engineers use when making calculations? Find your Birthday in Pi How old are you in Pi-years? Pi Planet. 6 Things You Probably Didn't Know About Pi by Wired Try to figure out how up to 612,330 digits are encoded in this picture! The Beauty of Pi Visualizing Pi by Ken Flerlage Art of Pi - 100 000 Digits of Pi Sound of Pi Do you wanna play Dart to calculate Pi? Pi Me A River Calculate Pi with Buffon’s Needles Plat Catch me if you can! to calculate Pi in t Taxicab Geometry Lunes (Crescents) of Hippocrates Pi in Rhind Papyrus Archimedes' Approximation of Pi Ramanujan's Strange Formula for Pi Estimating Pi using the Monte Carlo Method Pi o'clock and many more surprising problems by the mathedideas blog Join the Pi Day Challenge of NASA Pi TV Brilliant Pi Videos Pi TV Play Video Play Video 05:48 Calculating Pi with Darts Subscribe to Veritasium http://youtube.com/veritasium Instagram: http://instagram.com/thephysicsgirl Physics Girl: http://physicsgirl.org/ Facebook: http://facebook.com/thephysicsgirl Twitter: http://twitter.com/thephysicsgirl Help us translate our videos! http://www.youtube.com/timedtext_cs_panel?c=UC7DdEm33SyaTDtWYGO2CwdA&tab=2 Pi can be calculated using a random sample of darts thrown at a square and circle target. The problem with this method lies in attempting to throw "randomly." We explored different ways to overcome our errors. A million thanks to Derek Muller of Veritasium for his help with this video. http://youtube.com/veritasium. Also a huge thank you to Dan, Virginia, Lara and Cyrus for providing a yard. Play Video Play Video 06:28 Pi me a River - Numberphile How the length (and sinuosity) of rivers relates to Pi - featuring Dr James Grime. More links & stuff in full description below ↓↓↓ More on Pi from Numberphile: http://bit.ly/PiNumberphile The paper in Science (abstract): http://bit.ly/1m1j79B James Grime: http://singingbanana.com Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile Play Video Play Video 16:55 Calculating π by hand: the Chudnovsky algorithm For Pi Day 2018 I calculated π by hand using the Chudnovsky algorithm. https://en.wikipedia.org/wiki/Chudnovsky_algorithm k = 0 42698672/13591409 = 3.141592|751... k = 0 and k = 1 42698670.666333435968/13591408.9999997446 = 3.14159265358979|619... Watch me do the second term working out on my second channel: https://youtu.be/I7YvD7dqsy8 See me do the entire final calculation again (without a mistake) on Patreon: https://www.patreon.com/posts/17542566 Proof that I did actually do it properly: https://www.dropbox.com/s/64vc5iz7yt41r53/chudnovsky-pi-FIXED.pdf?dl=0 This was my attempt two years ago. Look at how much hair I had! https://www.youtube.com/watch?v=HrRMnzANHHs The Chudnovsky Brothers used their algorithm to be the champion pi calculators of the early 1990s: going from half a billion to four billion digits of pi. https://en.wikipedia.org/wiki/Chronology_of_computation_of_%CF%80 This video was filmed at Queen Mary University of London. CORRECTIONS - None yet. Let me know if you spot anything! Thanks to my Patreon supporters who enable me to spend a day doing a lot of maths by hand. Here is a random subset: Christopher Samples Sean Dempsey-Gregory Emily Dingwell Kenny Hutchings Rick de Bruijne Support my channel and I can make more videos: https://www.patreon.com/standupmaths Music by Howard Carter Filming and editing by Trunkman Productions Audio mastering by Peter Doggart Design by Simon Wright MATT PARKER: Stand-up Mathematician Website: http://standupmaths.com/ Maths book: http://makeanddo4D.com/ Nerdy maths toys: http://mathsgear.co.uk/ Play Video Play Video 08:24 Pi is Beautiful - Numberphile With thanks to Martin Krzywinski and Cristian Ilies Vasile - cool visualisers of Pi. More links & stuff in full description below ↓↓↓ Pi Visualisations (you can buy them too): http://bit.ly/PiBeauty Images used with permission. This video features Dr James Grime: https://twitter.com/jamesgrime More Pi videos from Numberphile: http://bit.ly/PiNumberphile Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile Play Video Play Video 18:40 The Discovery That Transformed Pi For thousands of years, mathematicians were calculating Pi the obvious but numerically inefficient way. Then Newton came along and changed the game. This video is sponsored by Brilliant. The first 314 people to sign up via https://brilliant.org/veritasium get 20% off a yearly subscription. Happy Pi Day! (for a few days ago...) References: Arndt, J., & Haenel, C. (2001). Pi-unleashed. Springer Science & Business Media — https://ve42.co/Arndt2001 Dunham, W. (1990). Journey through genius: The great theorems of mathematics. Wiley — https://ve42.co/Dunham1990 Borwein, J. M. (2014). The Life of π: From Archimedes to ENIAC and Beyond. In From Alexandria, Through Baghdad (pp. 531-561). Springer, Berlin, Heidelberg — https://ve42.co/Borwein2012 Special thanks to Alex Kontorovich, Professor of Mathematics at Rutgers University, and Distinguished Visiting Professor for the Public Dissemination of Mathematics National Museum of Mathematics MoMath for being part of this Pi Day video. Special thanks to Patreon supporters: Jim Osmun, Tyson McDowell, Ludovic Robillard, jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Lyvann Ferrusca, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal Written by Derek Muller and Alex Kontorovich Animation by Ivy Tello Filmed by Derek Muller and Raquel Nuno Edited by Derek Muller Music by Jonny Hyman and Petr Lebedev Additional Music from https://epidemicsound.com "Particle Emission", "Into the Forest", "Stavselet", "Face of the Earth", "Firefly in a Fairytale" Thumbnail by Gianmarco Malandra and Karri Denise Play Video Play Video 15:16 Why do colliding blocks compute pi? Even prettier solution: https://youtu.be/brU5yLm9DZM Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/clacks-thanks Home page: https://www.3blue1brown.com Many of you shared solutions, attempts, and simulations with me this last week. I loved it! You all are the best. Here are just two of my favorites. By a channel STEM cell: https://youtu.be/ils7GZqp_iE By Doga Kurkcuoglu: http://bilimneguzellan.net/bouncing-cubes-and-%CF%80-3blue1brown/ And here's a lovely interactive built by GitHub user prajwalsouza after watching this video: https://prajwalsouza.github.io/Experiments/Colliding-Blocks.html NY Times blog post about this problem: https://wordplay.blogs.nytimes.com/2014/03/10/pi/ The original paper by Gregory Galperin: https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf For anyone curious about if the tan(x) ≈ x approximation, being off by only a cubic error term, is actually close enough not to affect the final count, take a look at sections 9 and 10 of Galperin's paper. In short, it could break if there were some point where among the first 2N digits of pi, the last N of them were all 9's. This seems exceedingly unlikely, but it quite hard to disprove. Although I found the approach shown in this video independently, after the fact I found that Gary Antonick, who wrote the Numberplay blog referenced above, was the first to solve it this way. In some ways, I think this is the most natural approach one might take given the problem statement, as corroborated by the fact that many solutions people sent my way in this last week had this flavor. The Galperin solution you will see in the next video, though, involves a wonderfully creative perspective. If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Play Video Play Video 19:04 Why is pi here? And why is it squared? A geometric answer to the Basel problem A most beautiful proof of the Basel problem, using light. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/basel-thanks This video was sponsored by Brilliant: https://brilliant.org/3b1b Brilliant's principles list that I referenced: https://brilliant.org/principles/ Get early access and more through Patreon: https://www.patreon.com/3blue1brown The content here was based on a paper by Johan Wästlund http://www.math.chalmers.se/~wastlund/Cosmic.pdf Check out Mathologer's video on the many cousins of the Pythagorean theorem: https://youtu.be/p-0SOWbzUYI On the topic of Mathologer, he also has a nice video about the Basel problem: https://youtu.be/yPl64xi_ZZA A simple Geogebra to play around with the Inverse Pythagorean Theorem argument shown here. https://ggbm.at/yPExUf7b Some of you may be concerned about the final step here where we said the circle approaches a line. What about all the lighthouses on the far end? Well, a more careful calculation will show that the contributions from those lights become more negligible. In fact, the contributions from almost all lights become negligible. For the ambitious among you, see this paper for full details. If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue1Brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown Reddit: https://www.reddit.com/r/3Blue1Brown Play Video Play Video 17:17 Ramanujan's infinite root and its crazy cousins In this video I'll talk about Ramanujan's infinite roots problem, give the solution to my infinite continued fraction puzzle from a couple of week's ago, and let you in on the tricks of the trade when it comes to making sense of all those crazy infinite expressions. Featuring guest appearances by Vihart's infinite Wau fraction, the golden ratio and the Mandelbrot set. Here is a link to a screenshot of Ramanujan’s original note about his infinite nested radical puzzle: http://www.qedcat.com/misc/ram_incomplete.jpg Check out the following videos referred to in this video: https://youtu.be/jcKRGpMiVTw Mathologer video on Ramanujan and 1+2+3+...=-1/12. This one also features an extended discussion of assigning values to infinite series in the standard and a couple of non-standard ways https://youtu.be/CaasbfdJdJg Mathologer video on infinite fractions and the most irrational of all irrational numbers. https://youtu.be/9gk_8mQuerg Mathologer video on the Mandelbrot set. The second part of this one is all about a supernice way of visualising the infinite expression at the heart of this superstar. https://youtu.be/GFLkou8NvJo Vi Hart's video on the mysterious number Wau, a must-see :) Enjoy :) Play Video Play Video 23:20 Pi is IRRATIONAL: animation of a gorgeous proof NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) This video is my best shot at animating and explaining my favourite proof that pi is irrational. It is due to the Swiss mathematician Johann Lambert who published it over 250 years ago. The original write-up by Lambert is 58 pages long and definitely not for the faint of heart (http://www.kuttaka.org/~JHL/L1768b.pdf). On the other hand, among all the proofs of the irrationality of pi, Lambert's proof is probably the most "natural" one, the one that's easiest to motivate and explain, and one that's ideally suited for the sort of animations that I do. Anyway it's been an absolute killer to put this video together and overall this is probably the most ambitious topic I've tackled so far. I really hope that a lot of you will get something out of it. If you do please let me know :) Also, as usual, please consider contributing subtitles in your native language (English and Russian are under control, but everything else goes). One of the best short versions of Lambert's proof is contained in the book Autour du nombre pi by Jean-Pierre Lafon and Pierre Eymard. In particular, in it the authors calculate an explicit formula for the n-th partial fraction of Lambert's tan x formula; here is a scan with some highlighting by me: http://www.qedcat.com/misc/chopped.png Have a close look and you'll see that as n goes to infinity all the highlighted terms approach 1. What's left are the Maclaurin series for sin x on top and that for cos x at the bottom and this then goes a long way towards showing that those partial fractions really tend to tan x. There is a good summary of other proofs for the irrationality of pi on this wiki page: https://en.wikipedia.org/wiki/Proof_that_π_is_irrational Today's main t-shirt I got from from Zazzle: https://www.zazzle.com.au/25_dec_31_oct_t_shirt-235809979886007646 (there are lots of places that sell "HO cubed" t-shirts) lf you liked this video maybe also consider checking out some of my other videos on irrational and transcendental numbers and on continued fractions and other infinite expressions. The video on continued fractions that I refer to in this video is my video on the most irrational number: https://youtu.be/CaasbfdJdJg Special thanks to my friend Marty Ross for lots of feedback on the slideshow and some good-humoured heckling while we were recording the video. Thank you also to Danil Dimitriev for his ongoing Russian support of this channel. Merry Christmas! Load More Shop π ng for π Mathfan is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for us to earn fees by linking to Amazon.com and affiliated sites. SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP SHOP

- Math & Magic | MATH FAN
Math Fan Content Lessons Tasks Math Club Projects Math Magic and Illusions Math @ Home Math Magic Games & Puzzles Math & Art Easy tricks that you can amaze your friend and students 1. The Famous Mystery Calculator Trick Ask your friend to choose a number [1-63]. Show them each card here in turn and ask them if their number appears on it. You can guess the number by adding the top left corner numbers of each card that has their number. Can you find the trick? The first hint is if you have one more card, your friend can pick a number [1 - 127] Can you guess it now? Another hint is 1 appears only on the first of the cards and 63 appears on them all. ... Yes, It is the Binary way of writing the number - each card is the binary digit represented by the top left corner number. (Cards are not in exact order to create the mystery!) 63 = (1 + 4 + 16 + 2 + 8 + 32) 1 1 1 1 1 1 (in all 6 cards) 23 = (1 + 4 +16 + 2) so only in first four cards. 2. How math helps to create optical illusions Click here to view the interactive illusion exhibit where you can try the illusions on your own!

- Lessons | MATH FAN
Lessons Tasks Math Club Projects Math @ Home Math Magic Games & Puzzles Math & Art Lesson Plans, Ideas, Activities Winter Games Lesson ideas and great resources for the last days of the year Halloween Math Model Spider Webs using Math and many more surprises Origami in Space Origami in Space, Miura, and Trease folds and more Fractals Fractals are not only about self similarity but also fractional dimensions and measure of roughness Vedic Math Introduction to Vedic Mathematics Pascal Triangle Mathematical Secrets of Pascal Triangle - Task Cards Star Wars Math Celebrate 4th of May or use for Halloween. Star Wars themed math activities Optical Illusion How to create optical illusions using Google Slides Misleading Graphs Making informed decisions with Verified Data Diagonals of Rectangles Diagonals of Rectangles Investigation based on the least common multiple LCM concept. Cryptology CEASER CIPHER task cards Spirographs Spirograph Investigation about the radius of the fixed disc or wheel, (the number of teeth), the radius of the revolving disc, and the location of the pen (point) on the moving disc. Project Archimedes Project Archimedes Infinity Hotel Countability and the Hilbert's infinity Hotel Paradox Task A closer look to Cube A Cube Investigations about surface area and volume, numbers, 3d modeling, probability, and fractals. Exponential Growth An easy exponential growth task to prove vampires do not exist Prime Numbers Prime Numbers and The Cicadas 17-year Life Cycle Task Lattice Squares Number of Lattice Squares Puzzle-like Task Create a Math Clock Creating a Math clock using a blank clock template - Fractions and Angles Fibonacci Sequence Fibonacci Sequence Tasks with Polypad Clock Angles A Polypad activity to find the angles between the hour and minute hand of a clock Egyptian Fractions A lesson plan to explore the way that Ancient Egyptians using unit fractions to represent all the fractions. Recurring Decimals An Excel File to demonstrate the decimal parts of the fractions - The Source is anonymous Billiard Table Problem A great activity to explore the paths of billiard balls on a idealized pool table. Playground Math Playgrounds are the best places to explore math and physics. There are many activities with classical structures like swings, slides, and seesaws.