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  • MATH & SCIENCE DAYS TO CELEBRATE Celebrating birthdays of the great mathematicians and scientists as well as the national and global days related with math & science can motivate kids by increasing their science literacy and their engagement to the content. Click here for the calendar posters. Those celebrations can be used as an exciting start (warm-up) for that day’s lesson. a part of math & science club curriculum. a mini poster-questions like the ones I have posted above. Click to download poster 1 and 2 a long-term project topic for kids to complete and create a math/science calendar. a collaborative class project for the first lesson of each month. JANUARY 4th of January: Sir Isaac Newton's birthday English physicist and mathematician, who was the culminating figure of the Scientific Revolution of the 17th century Resources: 27th of January: Lewis Carroll's Birthday The famous English author of Alice's Adventures in Wonderland and its sequel Through the Looking Glass was also a brilliant scholar. He taught math and logic at Oxford, for many years. His real name is Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898). Here are some resources to celebrate his life; The Lewis Carrol Society of North America Alice's adventures in algebra: Wonderland solved by NewScientist Alice's Adventures in Wonderland: 150th Anniversary Edition Lewis Carroll's Puzzles LC logic puzzle by The Guardian. 28th of January: National Data Privacy Day Encourage students to clean up their virtual identities and improve their online security measures and learn more about cyber safety and cyber ethics. Resources: Ignition – Digital Citizenship. C-Save FEBRUARY 7th of February: e Day / Euler's Day In mathematics, Euler's constant is the base of the logarithm and is represented by "e" which equals approximately 2.71828. This, naturally, means that Feb. 7th is "e" day – Resources: Happy e-day from Wired: 11th of February: Women in Science Day Celebrate by reading the book “Women in Science” by Rachel Ignotofsky with kids, making an exhibit from the free posters of March for Science Beyond Curie Project by Amanda Phingbodhipakkiya making an exhibit from the free posters of NASA List of 70 books 70 Books to Inspire Science-Loving Girls ordering the movie of Maryam Mizrakhani “Secrets of the Surface “ from zalafilms 12th of February: Darwin Day The theory of evolution by natural selection that was developed by Charles Darwin revolutionized the study of living things. In his Origin of Species(1859) he provided a scientific explanation of how the diverse species of plants and animals have descended over time from common ancestors. His theory remains central to the foundations of modern biology. Resources 14th of February: Valentines Day Valentines Day is here only because I have found these math cards on the web. 😁Thanks to Cassandra Valenti (@MathWithMrsV) . Click here for the cards. Science Valentines Cards 15th of February: Galileo Galilei’s birthday A Pioneer in Mathematics, Physics, and Astronomy Resources Have a virtual visit to Galileo Museum in Florence Story of the Galileo's Compass See the Sector compass closer at Google Arts and Culture 19th of February: Nicolaus Copernicus's birthday A Renaissance astronomer and mathematician who sparked the revolution in cosmology that's still going on today Resources: Mathematical Treasure: Copernicus' De Revolutionibus Copernicus' Life by the Stanford Encyclopedia of Philosophy 29 of February: Leap Day Every four years, during a leap year, the imperfect match between the length of a calendar year and Earth's orbit results in an interesting calendar adjustment known as a leap day. In this problem set, students calculate the difference between the calendar year and Earth's orbital period, determine how much extra time gets added to our calendar, and identify which years omit leap years. Resources: Leap Day Math by NASA Time &The Maya Calendar MARCH 8th of March: International Women's Day and Women History Month - Watch Secrets of Surface; Check local listings and airdates page. - Check out the all-female version of Mathigon's timeline of mathematics. - 32 Posters of Badass Women in Science to Inspire Girls Today - A must-visit blog A Mighty Girl! - Visit the Mathfan Pages for posters, books and movies about the women of science! 14th of March: Pi Day and International Math Day Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π”) is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159. The theme for the 2022 International Day of Mathematics is Mathematics Unites Resources: 18th of March: Christian Goldbach' s Birthday 18 March 1690 marks the birthday of Christian Goldbach who studied law and mathematics and best known for the conjecture he made in a letter to Euler that every even integer > 2 is a sum of two primes. Watch Professor David Eisenbud on the famed Goldbach Conjecture on YouTube. Try Goldbach Calculator by Mathigon Read the book Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis More on Goldbach Conjecture on AoPS 22nd of March: World Water Day World Water Day 2020, on 22 March, is about water and climate change – and how the two are inextricably linked. Resources: Oil Spill Clean Up Simulation Watch the documentary A Plastic Ocean 28th of March: Earth Hour Started by WWF and partners as a symbolic lights-out event in Sydney in 2007, Earth Hour is now one of the world's largest grassroots movements for the environment, engaging millions of people in more than 180 countries and territories. It has become a catalyst for positive environmental impact, driving major legislative changes by harnessing the power of the people. Watch the video "Rock the World" on YouTube Resources: 31st of March: Descartes' Birthday The first modern philosopher is also famous for having made an important connection between geometry and algebra, which allowed for the solving of geometrical problems by way of algebraic equations. APRIL 15th of April: Leonardo Da Vinci's Birthday Several activities, projects, tasks can be done about Da Vinci, understanding his vision and polymath personality is very important in STEAM education. There will be a detailed Da Vinci Section at funmathfan. Coming Soon .. 22nd of April: Earth Day 04.22.2020 marks 50 years of Earth Day. The theme for Earth Day 2020 is climate action. Since Climate change represents the biggest challenge to the future of humanity and the life-support systems that make our world habitable. Earth Day was a unified response to an environment in crisis — oil spills, smog, rivers so polluted they literally caught fire. On April 22, 1970, 20 million Americans — 10% of the U.S. population at the time — took to the streets, college campuses and hundreds of cities to protest environmental ignorance and demand a new way forward for our planet. 25th of April: DNA Day National DNA Day is a holiday celebrated on April 25. It commemorates the day in 1953 when James Watson, Francis Crick, Maurice Wilkins, Rosalind Franklin and colleagues published papers in the journal Nature on the structure of DNA. Essay Contest April 27-May 3, 2020 Astronomy Week 10 Astronomy events in 2020 30th of April: Gauss' Birthday German mathematician Carl Friedrich Gauss was so proficient at mathematics that he is considered to be one of the greatest mathematicians of all time. He was also talented in other subjects, including cartography, physics, and planetary astronomy MAY 4th of May: STAR WARS Day May the Fourth Be with You! Here is a list of math&science activities you can use for Star Wars Day. 11th of May: Salvador Dali's and Richard Feynman's Birthdays Salvador Dali and Mathematics Dali's Hypercube: Scientific American , Dali and the 4th Dimension by Thomas F. Banchoff Richard P. Feynman Biographical by the Nobel Prize Feynman Lectures and his official site 12th of May: Women in Mathematics Day (Birthday of Maryam Mirzakhani) May 12 was chosen for the Celebration of Women in Mathematics because it is the birthdate of Maryam Mirzakhani. Watch Secrets of Surface; Check local listings and airdates page. Here is the trailer. Watch a 5-min Maryam Mirzakhani documentary by the Simons Foundation and International Mathematical Union. Read the touching tribute by Stanford University for Maryam Mirzakhani and learn about her latest works. Visit for details. 2022 Events List for May 12 from all over the world. Visit the Committee for Women in Mathematics page. It is also the birthday of Florence Nightingale Visit the page "FLORENCE NIGHTINGALE: THE PIONEER STATISTICIAN" by the Science Museum UK to learn more about how she used the data to save more lives. Watch Florence Nightingale: Joy of Stats by the Open University Check out the all-female version of Mathigon's timeline of mathematics. 32 Posters of Badass Women in Science to Inspire Girls Today A must-visit blog A Mighty Girl! Visit the Mathfan Pages for posters, books and movies about the women of science! 18th of May: Bertrand Russell's Birthday The British philosopher, mathematician, author and Nobel Prize Winner (Literature) Bertrand Russell's birthday can be used to introduce Paradoxes. Visit and watch the video from Up and Atom about Russell's Paradox JUNE 5th of June: World Environment Day United Nations leads the organizations and celebrations of WED to encourage awareness and action for the protection of the environment with a different theme every year since 1974. Visit the official website 2020 theme of WED: Time for Nature - Biodiversity (You can also take the quiz on UN's webpage about biodiversity) 2019 theme of WED: Beat Air Pollution 8th of June: World Oceans Day Around 70% of Earth's surface is covered with oceans. But understanding the right amount of water, we need to calculate the volume of the water not the surface area. Watch the video "All the Water on Earth" to raise awareness for the oceans. Click here for the SA:V poster. You can plan your own event as well as joining one nearby to support the World Oceans Day. Visit the official website 13th of June: Nash's Birthday Celebrate the life of the only person who received both the Nobel Prize and Abel Prize. 2015 Abel Prize is for his seminal work in partial differential equations and the 1994 Nobel Prize is for his work in economics. Watch the movie "The Beautiful Mind" where Nash is portrayed by Russel Crowe. The Movie is mostly concentrated on his contributions to Game theory and Economics. Some videos to check out about Game Theory and Prisoner's Dilemma by SciShow by Up and Atom 17th of June: M.C. Escher's Birthday The Dutch artist Escher is one of the symbols of math and art intersection. He is particularly famous with his tessellations, polyhedra drawings, hyperbolic geometry, or impossible shapes. There is an Escher Museum in DenHag / Holland which displays the great examples of his work. You can visit the Museum's Website and have a VR tour to see some of Escher's great work. Also try the Online Tessellation Applet by and to learn more about the tessellations and their properties visit Mathigon's Tessellation Chapter. 19th of June: Blaise Pascal's Birthday He invented one of the first mechanical calculators when he was still a teenager, worked on geometry, probability, physics and theology, and is remembered for naming Pascal’s Triangle For his philosophical approaches watch the video by wireless philosophy and for his inventions, you may watch the video by Da Vinci Kids 23rd of June: Alan Turing's Birthday As one of the most outstanding people in human history, British Mathematician Alan Turing is also a computer scientist, philosopher, code-breaker. His 1950 paper on 'Computing Machinery and Intelligence’ gave birth to todays' concepts of AI and machine learning. Visit the website of Alan Turing Institute in UK. You may also watch the 2014 Movie "The Imitation Game" based on the biography of Alan Turing: The Enigma. 28th of June: Happy Perfect Number Day! Perfect numbers are defined as positive integers that are equal to the sum of all their positive divisors except themselves. 6 = 1+2+3 and 28 = 1+2+4+7+14 Visit the Mathigon's Perfect number chapter to learn about the perfect numbers. JULY 1st of July: Leibniz's Birthday The Universal Genius, Gottfried Wilhelm Leibniz, invented calculus (together with Newton) as well as mechanical calculators, and he was a prominent German polymath and one of the most important logicians, mathematicians and natural philosophers of the Enlightenment. You may watch the video by Crash Course ''Newton vs Leibniz" 22nd of July: 22/7 Pi Approximation Day If 14th of March is not enough for you to celebrate Pi, you may continue to celebrate on the best approximation day too. You may watch the video by Draw Curiosity about the different approximations of Pi. AUGUST 4th of August: John Venn's Birthday English mathematician and logician John Venn was born in 1834. He is especially famous for introducing the "Venn diagrams" used in set theory and logic. Venn Diagram uses circles to visually and logically sort groups to illustrate their relationships to each other. SEPTEMBER 8th of September: Marin Mersenne's Birthday Although he was a famous polymath contributed many different fields from math to music, he is best known with his discovery about prime numbers. Mersenne Primes are the numbers that can be written in the form Mn = 2^n − 1 where n is a prime. The first four Mersenne primes are M2 = 3, M3 = 7, M5 = 31 and M7 = 127. You can visit the website and join the Great Internet Mersenne Prime Search (GIMPS). 17th of September: Riemann's Birthday Georg Friedrich Bernhard Riemann as a German mathematician who made contributions to analysis, number theory, and differential geometry. Riemann Integral, his work on Fourier Series and Riemann Surfaces are one of the most influential works of mathematics. Solving the Riemann Hypothesis is called "the hardest way to earn a million dollars"! You may want to watch the related Numberphile video. There is also a more advanced video by MoMath "Math Encounters - Primes and Zeros: A Million-Dollar Mystery" 22nd of September: Michael Faraday's Birthday His main discoveries include the principles underlying electromagnetic induction, magnetism and electrolysis. Although Faraday received little formal education, he was one of the most influential scientists in history. Albert Einstein kept a picture of Faraday on his study wall, alongside pictures of Newton and Maxwell. You may watch the videos from OpenMind and SciShow to talk about Faraday OCTOBER 4-10 October: World Space Week: This year the theme is “Satellites Improve Life.” In 2021, World Space Week celebrates “Women in Space.” Week of 4 - 10 October is declared as World Space Week to celebrate each year at the international level the contributions of space science and technology to the betterment of the human condition” You may visit the official website 9-15 October: Earth Science Week: Earth Science Week 2020 Theme is 'Earth Materials in Our Lives'. You may visit the official website and choose an activity categorized according to the different grade levels. There are also different contests like essay, photograph, visual arts and video that each grade level can join. 31 October: Halloween Here is a list of math & science activities for Halloween with additional surprises. NOVEMBER 7th of November: Marie Curie's Birthday Marie Curie is the first woman to win a Nobel Prize, in Physics. She also became the first person to claim Nobel honors twice in different fields (Chemistry). With her husband, they discovered polonium and radium, and she led the development of X-rays and treatment of cancer. Watch the video by SciShow about Curie. There is also a 2019 movie called Radioactive starring Rosamund Pike as Marie Curie. Curie’s laboratory notebooks are at France’s Bibliotheque National in Paris. You can view her notebooks by signing a a liability waiver and wearing protective gear since these items are still radioactive . Click here for the Marie Curie poster. Some of her famous quotes: "Life is not easy for any of us. But what of that? We must have perseverance and above all confidence in ourselves. We must believe that we are gifted for something and that this thing must be attained." "Nothing in life is to be feared; it is only to be understood." "Be less curious about people and more curious about ideas." Here is a virtual exhibit you can visit by the University of Paris about Maria S. Curie (1867-1934) 11th of November: Origami Day One of the best days to celebrate and relax at the same time is for sure the Origami Day. You can start visiting the official website of the Origami day in USA. There are several books about Origami. I can recommend one particular book about modular origami by the inspiring young writer Byriah Loper is "Mind-Blowing Modular Origami: The Art of Polyhedral Paper Folding: Use Origami Math to fold Complex, Innovative Geometric Origami Models" You can also learn more about the Origami axioms and applications by visiting Mathigon website. Origami folding techniques are used in spacecrafts as well. If you are looking for a more STEAM related ideas, here is the funmathfan's ORIGAMI IN SPACE; MIURA, TREASE AND MORE article. 23rd of November: Fibonacci Day November 23rd, corresponds to the first numbers of the Fibonacci sequence 11.23 = 1 – 1 – 2 – 3 – 5 - 8 - 13 - 21 - 34 - ... This pattern of counting means that each number is the sum of the previous two. DNA patterns and hurricanes contain patterns showing this sequence. It is referred as the “nature’s secret code” . Some say the famous Apple logo's design is based on the Fibonacci series too. Here are three different math tasks with Polypad related with Fibonacci Numbers Brick Walls and Fibonacci Number Bars and Fibonacci Number Sequences Visit the website by Dreambox OR Mensa for Kids to celebrate the Fibonacci Day DECEMBER 10th of December (October 12): Ada Lovelace Day English mathematician and writer Ada Lovelace is also one of the first computer programmers. She is the daughter of famous poet Lord Byron. In her notes, Ada Lovelace explained the difference between the Analytical Engine and previous calculating machines, particularly its ability to be programmed to solve problems of any complexity. She was aware of the potential of the device extended far beyond mere number crunching they can be used to solve advanced algorithms. You may watch the videos by Da Vinci TV and SciShow to learn more about Ada Lovelace. Click here for the Ada Lovelace poster. 7 - 13 December: Computer Science Education/Hour of Code Week Visit the official websites to raise awareness about the Computer Science and coding. CS Ed Week: Hour of Code: You can promote computer science locally, host a CS Tech Jam or bring Hour of Code to your classroom. Remember that, even if you cannot provide computers or tablets for everyone, you can use Computer Science Unplugged Activities to introduce the concepts of CS without using computers. 22nd of December: Ramanujan’s Birthday and Indian National Math Day Here is a Google slide with many links to celebrate the life of Ramanujan. Extra: - Read the remembrance by his collaborator G.H. Hardy: The Indian Mathematician Ramanujan - A poem by Jay Cummings: Joined by Math HAPPY HOLIDAYS 26th of December: Conway’s Birthday John Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He is the inventor of cellular automation and the zero-player game; Game Of Life. - Play Game of Life by Conway - Watch the series of Numberphile interviews with Conway on YouTube. 27th of December: Kepler’s Birthday Kepler was a German teacher, astronomer, mathematician, and astrologer. He is best known for his laws of planetary motion. Watch the video about his three laws of planetary motion. You can visit the Nasa's education website for the activity "Exploring Exoplanets with Kepler" He was also the first person to publish a detailed study of the tilings of regular polygons in Book II of Harmonices Mundi ("The Harmony of the World"), published in 1619. Here is the Polypad activity where you can draw Kepler's monsters (fused decagon pairs)

  • Vedic Squares & Vedic Worms, Spirolaterals

    IDENTIFYING THE PATTERNS OF MULTIPLICATION TABLE Can you draw the picture of the multiplication table? What if I tell you the images below are the multiplication table itself? Let’s how we can create our own multiplication art! Part I: 1. Fill in the multiplication table grid below. 2. Reduce double-digit numbers to a single digit by adding the digit of the products. Example: If 9×9=81, add the numbers in the sum (8+1), and put the sum of 9 in the square. If the new sum is also double-digit, add those numbers. Example: 7×8=56; 5+6=11; 1+1=2. Place the number 2 in that square. 3. Assign a color to each number and fill them accordingly. For example: All number 1 boxes may be blue, number 2 boxes may be green, and so on. 4. ART: You now created one quarter of the Vedic square. Reflect the square with respect to the vertical axis, then select both to reflect wrt the horizontal axis to complete your Vedic Square. Even vs Odd Tech Help: You can use Spreadsheets like MS Excel, Numbers , Google Sheets and use Conditional Formatting to create your designs, then by using lots of different options you can create the reflections of your initial image. (The easiest is copy /paste and flip your image!) Discussion Questions: Historically the Vedic square was not produced on the computer, how has technology changed the way art is done and how do you think technology has affected other areas of art? Discuss the origins of Islamic art and talk about similarities and differences in art from various cultures around the world. Search Web to see the Vedic Art examples at art and architecture. Part II : Connect the Dots: Some obvious patterns will be seen after connecting some specific numbers like; all 2’s, all 3’s, all 4’s and so on. What patterns did you realize? Resemblances and differences among the patterns the numbers formed? Part III : How to Make a Spirolateral Spirolaterals are geometrical figures formed by the repetition of a simple rule. The pattern is formed by drawing line segments of a certain length from a number sequence with a fixed angle and a direction. Although the spirolaterals can be created with any number sequence, we will use the Vedic Squares we have created at Part I. That’s why they are also called “VEDIC WORMS”. 1. Start with a row of numbers you choose. (1,2,3,4,5,6,7,8,9) These numbers will determine the length of each ‘step’ of the ‘spirolateral’. 2. Choose a direction; clockwise (CW) or counterclockwise (CCW) 3. Choose a grid type to draw on (In fact here, you are choosing the angle of your movement) a. Square Grid (90 degrees ) b. Isometric Grid (60 degrees ) c. Hexagonal Grid (120 degrees ) … 4. Now start drawing spirals through your list. For example, if we choose CW direction on a square grid with the first row of numbers, It means 1 step up, 2 steps right, 3 steps down and 4 steps left then repeat like 5 steps up, 6 steps right, 7 steps down and 8 steps left and 9 steps up to complete your drawing. 5. Continue until you return to the start or you are convinced that your spirolateral will never return to the start. Tech help: Use the Polypad Canvas here to create your multiplication table Spirolaterals Here is A 3D version of the 1-2-3-4-5-6-7-8-9 spirolateral. You can use the same Polypad canvas to create 3D Vedic spirolaterals using the other rows. You can also use GeoGebra to draw the spirolaterals on different grids. Do not forget to select the “snap to grid” option to create accurate drawings. Mathematical Notation: This shape is 3 sub 36. It means, the pattern is formed by a series of 3 steps of length “1, 2, 3” with a 36˚ CW turn. You can use any angle you wish especially if you use a computer program to make the movements easier and quicker. After the hand drawings, try the spirolateral generator here to create your own multiplication table art. Discussion Questions: i. What kinds of symmetry do these shapes have? ii. Can I predict, from the numbers in the sequence, the kind of symmetry of a spirolateral or the number of cycles in a closed spirolateral? iii. What will happen if I use the same sequence, but always turn CW instead of CCW? iv. What combinations of number sequence and angle of turn create non-terminating patterns? v. If the angle of turn is 120˚, what number sequences give closed patterns? EXTRA: Create spirolaterals by using CLICK HERE TO DOWNLOAD THE PDF OF THE SPIROLATERAL INVESTIGATION WITH THE GRIDS Resources: Weisstein, Eric W. "Spirolateral." From MathWorld--A Wolfram Web Resource. Spirolateral Creator: NCETM secondary Magazine Issue 78 Robert J. Krawczyk, THE ART OF SPIROLATERALS , College of Architecture Illinois Institute of Technology To read the letter that Professor Frank Odds wrote to R.J. Krawczyk about the spirolaterals that he found at 1962, please visit The original article by Frank C. Odds ODDS, FRANK C. “SPIROLATERALS.” The Mathematics Teacher, vol. 66, no. 2, 1973, pp. 121–124. JSTOR, Accessed 29 Mar. 2020.

  • Spirograph

    As we all know through play, kids learn different things without even realizing it! Playing with a spirograph, experimenting and trying all kinds of combinations, kids will develop mathematical and scientific intuition they can draw and realize the patterns, with the proper questions they can experiment, hypothesize, test, and generalize even reach conclusions. Spirograph is a geometric drawing device that produces various mathematical curves known as hypotrochoids and epitrochoids. The well-known toy version was developed by British engineer Denys Fisher and first sold in 1965. Original toy’s website: This image is taken from Smithsonian National Museum of American History MATH: The patterns that are created depend on three variables: the radius of the fixed disc or wheel, (the number of teeth) the radius of the revolving disc, (the number of teeth) the location of the point on the moving disc. By changing any one of these variables you can get tons of incredible and beautiful patterns. Please check the Wolfram's collection of plane curves related with the curve names listed below. A point on a wheel rolling inside a circle traces out a hypocycloid. A point on a wheel rolling on a flat surface traces out a curve called a cycloid. A point on a wheel rolling outside another wheel traces out an epicycloid. A spirograph can be used to create artistically interesting patterns. Besides the serious math behind it, the patterns can also be used to study; LCM Modular arithmetic The fundamental theorem of mathematics. Use the spirograph applet here “" Click here for the SPIROGRAPH TASK about LCM and Modular Arithmetic (for the middle school level) ****** RESOURCES MATH BEHIND SPIROGRAPHS GEOGABRA APPLETS: Resources:

  • 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: ------ ------ ------

  • 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?

  • Net of a Sphere, Different Map Projections, Codex Atlanticus, and a Library in Italy

    We know that it is not possible to draw the net of a sphere like cylinders, cones, or polyhedra. So, how we can represent a 3D sphere on a 2D paper? Our world is pretty much a spherical shape too, then, how come we have so many different world maps? When we peel an orange, we cannot flatten the peels entirely on a two-dimensional surface (at least without deforming them!). Mathematician Hannah Fry explains and demonstrates the orange peel idea in the video of A Strange Map Projection. That's why the all the world maps are somewhat distorted. You may try to draw a rough world map on the orange and then peel it. Like you can peel an orange in different ways, there are different map projections for our spherical world. You can try the interactive by to see a few of these projections and how they distort the actual size and the locations of the continents. Many Mathematicians tried to converge the sphere to different polyhedra to draw it net, therefore the map of the world. For instance, Buckminster Fuller designed his map using triangles since he uses an icosahedron (A Platonic Solid with 20 triangular faces) as the main shape of our world. This projection style is called Dymaxion (Fuller) projection. One of the most famous polymaths of human history, Leonardo Da Vinci, used eight congruent Reuleaux Triangles* as the net of the sphere. Octant projection (1514), Leonardo da Vinci *A Reuleaux triangle is a shape with constant width like a circle formed by the intersection of three identical circles. To see the collection of all known notebooks of Da Vinci, please visit The notebook that we are looking for is “Codex Atlanticus”, and it is original pages are in this beautiful library in Milano; You may visit the Ambrosiana Library virtually using Google Arts and Culture. The better news is that we can find this 1119 page - notebook online and categorized as algebra, geometry, physics, natural sciences, etc ... The digital version of Codex Atlanticus. Another reason that this library is a sacred place for the mathematicians is, it also has the original copy of “Divina proportione” by the Italian Mathematician Luca Pacioli. Divina Proportione is about the mathematical and artistic proportion, golden ratio and its applications. While Pacioli was writing this book, Da Vinci was taking mathematics lessons from him. In the book, Da Vinci illustrated two views for the solid shapes; a solid view and a skeleton view where he removed the faces to better reveal the complete structure of the polyhedron. These sketches provide a complete view of the number of sides, faces and the vertices of the polyhedra. In terms of functionality, they serve the same purpose as the 2D Nets of the solids. Let's have a look how did Da Vinci sketch the sphere for Pacioli's book; ...and as we have started, we end up with an orange in our search of the net of a sphere.

  • Create Your Own Math Clock

    ETKİNLİĞİN TÜRKÇESİNİ PDF OLARAK İNDİREBİLİRSİNİZ. Unit: Mathematics of Timekeeping Activity: Create your own math clock Our goal is to write the numbers to the proper places of the blank clock. We can explore many mathematical concepts by using this activity. For thousands of years, devices have been used to measure and keep track of time. Sundials, pendulum clocks, hour glasses are used till the invention of mechanical clocks. Today atomic clocks are used to tell the time precisely. There is a very nice article and a video on “A History Of Timekeeping” Page by British Museum. You may also check the History of Timekeeping Devices on Wiki Essential Questions: Why 1 hour is 60 minutes? This question can lead a discussion about factors and multiples. What are the different number systems in human history (Babylonians to start with) that uses the sexagesimal counting system? Watch the video from Numberphile. The current sexagesimal system of time measurement dates to approximately 2000 BCE from the Sumerians. STEAM Connections: History of timekeeping Please watch the "A Brief History of Timekeeping" by SciShow. And read the article on Britannica for Kids or the article “A Chronicle Of Timekeeping” by Scientific American Search about different types of clocks; Sundials – Let’s make a sundial Water Clocks – Build your own water clock Hour clock Pendulum clocks Science; Invention of the mechanical clocks Mechanics of a clock – ready-to-use mechanism. For the image and explanations, please check Britannica for Kids. A blank wall clock Create Your Own Math Clock CONCEPT #1: FACTORS AND DIVISORS If you can divide a number A by a number B, without remainder, we say that B is a factor (or divisor) of A, and that A is a multiple of B. Factors always appear in pairs such as 12 = 1 x 12 12 = 2 x 6 12 = 3 x 4 1 and 12, 2 and 6, 3 and 4 are called the factor pairs. So, the whole list of factors of 12 is {1, 2, 3, 4, 6, 12} The factors of 60 are _________1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. The total number of factors is of 60 is ___12 CONCEPT #2: DIVISION AND FRACTIONS We can define the non-whole number quantities by using fractions and decimals. For instance, a half is represented as ½ whereas a quarter is represented as ¼. In fact, most of the numbers can be represented as fractions. 0.2= 1/5 0.333.. =1/3 0.142856.. = 1/7 1 = 1/1 = 2/2 =3/3 … 1.5= 3/2 =6/4= 15/10 .. 2= 2/1 = 4/2 = 6/3 .. When we say half an hour it means you have ___30 mins. A quarter of an hour is only ____ 15 mins. So half past ten: ____ 10:30 A quarter past three: _____ 3:15 A quarter to nine: _____8:45 CONCEPT #3: ANGLES We need to divide the blank circular clock into 12 equal parts to be able to insert the numbers. But how we can divide a circle into 12 equal pieces? It is time to explore angles. What are the types of angles? ______________ So we have a _____ 360 degrees angle to divide by ____ 12 It means, the circle will have numbers to represent hours in every _____ 30 degrees. There are 60 minutes in every hour. So the minute-hand needs have _____60 stops. Since 360 degrees : 60 = 6, we need to put a little mark on every_____ 6 degrees for the stops of the minute hand. To be able to measure any given angle or draw an angle with a given measurement we need to use the _________ protractor. Angle Measurement is a very important skill for all of us to grasp in early ages. If you need, lease watch the angle measurement video on YouTube “Drawing Angles With a Protractor”. Let’s start putting a mark in every 6 degrees. Do not worry we are going to do this only 60 times. Do not forget to insert hours in every 30 degrees. CONCEPT #4: CIRCLES Up to now, we have explored many concepts related with circles. To start with, we can figure out that all the points we have inserted on the circle are equidistant to its center. The set of all equi-distant points from a given point is called a _____ circle. The place we put our protractor to measure and draw the angles- which is exactly in the middle of the circle is called the ______ center of the circle. The hour marks are on the ___ arc of the circle. If we connect the center of the clock where we are going to insert the minute and hour hand and any mark on the arc, that segment is called the _____radius. Twice the radius is called _____ diameter. Diameter can help you to figure out the dimensions of your clock. The clock I have has a diameter of 24 cm. So on the wall, if I find a square 24 by 24, my clock will definitely fit in it. Each angle we measure is called the ______ central angle. These terms will also help us to communicate better. If you want to color your clock, you may need to calculate the area of the clock to see how much paint you will need. The length of the radius helps us here. The area of any circle is π times the square of its radius. To make a rough estimate, you may multiply the square of your clock’s radius by 3. When we insert the battery in, the clock starts ticking. That moment is the one that we can start talking about time measurement and all related problems. We can definitely raise this to make a fancy mathematical clock. Pick a number or use the numbers of your birthday and try to express 1- 12 in terms of the number(s) you choose. You can use all the operations you know. Mind the order of operation!

  • Matematik & Sanat; İlhan Koman

    Sanatı ve matematiği harmanlayarak en etkileyici örneklerini yaratan ünlü heykeltıraşımız İlhan Koman’ın seneye doğumunun 100. yılını kutlayacağız. Türk Da Vinci’si olarak anılan Koman, İstanbul’un simgelerinden biri olan Akdeniz Heykeli’nin de yaratıcısıdır. Edirne'de 2014 yılında adına bir müze de açılan İlhan Koman’ın çoğu eseri, yaşamının son yirmi yılında ailesiyle birlikte yaşadığı ve atölye olarak da kullandığı Hulda adlı teknesinde bulunmaktadır. Bu tekneden görüntülerin yer aldığı İz TV Sudaki İzler (88. Bölüm) ve 2010 yılında Arte İstanbul'da düzenlenen sergisinden görüntülerin yer aldığı bu videoyu izlemenizi öneririm. İlhan Koman’ın eserlerini incelediğinizde onları sanat eseri ya da bilimsel çalışma olarak ayrıştırabilmenin olanaksız olduğunu görürsünüz. Koman, heykellerini geliştirirken kullandığı matematik formülleri ile de çok iyi bir matematikçi olarak da bilinmektedir. ∏+∏+∏+∏+∏ Örneğin, birden fazla pi sayısı içeren yüzeyler yaratmak üzerine kurguladığı heykelde, dairenin çapını değiştirmeden, yüzeyini pi sayısının katları ile arttırılarak kıvrılmasıyla oluşan bir seri çalışma yapmıştır. Sonsuz sayıda pi kullanılınca, yüzeyler katlanarak, kavisler yaparak iç içe geçmiştir. Ortaya çıkan şekil, en dış yüzeyi ve merkezi birbirine bağlayan katmanlarca yüzeyden oluşan, baş döndürücü bir küre olmuştur. 1970’lerin sonları ile 1980’lerin başlarında üzerinde çalıştığı “Developable Forms” kategorisi içinde sayılan ∏+∏+∏+∏+∏ isimli bu çalışmaya ait sergi de yine Boğaziçi Üniversitesi Kütüphanesinde sergilenmektedir. Developable Sculptural Forms of Ilhan Koman Akgün, Tevfik et al. “Developable Sculptural Forms of Ilhan Koman.” (2006). Link Image attributions: Wolfram Demonstrations Wolfram demo’ ları arasında da Koman Surfaces ve Koman Variations isimli iki interaktif çalışma yeralmaktadır. "Bir balonun üzerine bir eğri çizin, eğri üzerindeki noktaları çizgilerle balonun ortasına bağlayın ve sonra balonu patlatın. Ortaya çıkan şekiller çok hoş ve sanatsal olabilir mi? İlhan Koman, bu yöntemi kullanarak çok zarif heykeller üretmiştir. Bu Demo, bu heykelleri oluşturmanıza ve daha sonra 3D olarak döndürmenize ve inceleyebilmenize olanak tanır. " Sonsuzluk Eksi Bir İlham Koman, maddenin ve doğanın içindeki sonsuz devinimin heykellerini yapmıştır. Koman’ın dinamik eserlerden oluşan Sonsuzluk Eksi Bir sergisi de yine bilim ve sanatın buluştuğu en güzel örneklere ev sahipliği yapmaktadır. Bu sergiye ait bir çok ürün dünyanın farklı yerlerinde sergilenmektedir. Rolling Lady Koman, Rolling Lady formunu 1980'lerin başında keşfetti. Bu form, iki tekerlek oluşturmak için birbirine yapıştırılmış dört koniden oluşur. Adından da anlaşılacağı gibi, bu heykel güzel bir hareketle yuvarlanabilir. Bu cismin kumun üzerinde ilerlerken çizebileceği yolu düşünün. Arte İstanbul Sergisinden Siz de bu hareketi gözlemleyebilmek için kendi modelinizi yapabilirsiniz. Rolling Lady’nin Thingiverse platformunda 3D Modeli bulunmaktadır. Bu modeli kullanarak kendi kopyanızı 3D Printer yardımı ile oluşturabilirsiniz. Hiperform Hiperformlar, Koman'ın keşfettiği en zarif ve anlaşılması zor formlardan biridir. En basit hiperformlar, dört eşit kareden oluşan dikdörtgenlerden oluşturulur, köşeleri 2π ve katları olacak şekilde bükülür ve birleştirilir. Aşağıdaki link den alınmış şekilde bu en basit hiperformların nasıl oluşturulacağını göstermektedir. Akgün, Tevfik et al. “Developable Sculptural Forms of Ilhan Koman.” (2006). Link Image attributions: İlhan Koman, ünlü Alman matematikçi Möbius’un sonsuzluk işareti olarak da kullanılan tanınmış Mobius bandını da yeniden yorumlamıştır. Arte İstanbul Sergisinden Koman’ın “Portal” (Ana Kapı) adlı heykeli İlhan Koman Vakfı tarafından 2008 yılında Boğaziçi Üniversitesi’ne bağışlanarak Kuzey Kampüsteki yerini almıştır. Bu kapının warehouse platformunda 3D modeli de bulunmaktadır. İlhan Koman’ı öğrencilerimize tanıtmak için kullandığımız sunuma da buradan ulaşabilirsiniz. Keynote, Pdf İLHAN KOMAN’IN ESERLERİ BUGÜN HANGİ MÜZELERDE? Stockholm Modern Müzesi (İsveç), MoMA (ABD, New York), Palais des Beaux Arts (Fransa, Paris), Seattle Art Museum (ABD, Seattle), Museo J. Batlle (Uruguay, Montevideo), Musee d’Art Moderne de la Ville de Paris (Fransa, Paris), İstanbul Resim Heykel Müzesi. 17 Haziran 2019’da Google’ın İlhan Koman Doodle’ı “Can science and art meet in one place?” asked Turkish artist İlhan Koman, born in Edirne on this day in 1921. “I'm trying to realize this meeting in sculpture… I'm trying to create new forms.” Today’s Doodle celebrates the multidisciplinary sculptor whose wide-ranging interests and endless experimentation with various media and techniques, as well as mathematical concepts, led some to call him the “Leonardo Da Vinci of Turkey.” As a child, Koman enjoyed playing with bolts and screws, and spent hours at a local blacksmith’s shop, watching the craftsman work with metal. When visiting relatives in the seaside city of Istanbul, he made models of ferry boats in the harbor and planned to become a shipbuilder before deciding to go to art school. Upon graduating from Istanbul’s Art Academy, he moved to Paris, where he studied during the 1940s, opened a workshop, exhibited his own abstract sculpture, and spent hours in the Louvre admiring the ancient Egyptian and Mesopotamian art and the work of modern masters such as Rodin, Brancusi, and Giacometti. While representing Turkey in the 1958 Brussels World's Fair, he met the architect Ralph Erskine, who invited him to work in Sweden. It was there that Koman would also teach at Stockholm’s Konstfack School of Applied Art. In the 1960s, he bought a two-masted wooden sailboat called the Hulda, which he adapted into a studio and living space. During his time in Sweden, Koman began what he called his ‘Iron Age,’ exploring the malleability of metal. He created many public works, the best known of which is the monumental sculpture Akdeniz in Istanbul. The 4.5 ton figure of a woman with outstretched arms was fashioned from 112 strips of metal. Kaynaklar: Akgün, Tevfik et al. “Developable Sculptural Forms of Ilhan Koman.” (2006).

  • Virtual STEAM Museums

    As you all know there are great math, science and technology museums all around the world. I have listed a few of them under the STEAM ITINERARIES page as well. Obviously we do not have time and money to visit all of them If you do not have the opportunity to travel so much but still want to see those museums or want to show them to your students to inspire, you can use Google's Art and Culture as an app or a website like you may use it for seeing the best artworks on earth. Let's start with DEUTSCHES MUSEUM from Munich, Germany As Europe’s largest technology museum, Munich’s Deutsches Museum is at the forefront of researching new modes of communication, transportation, and energy production. You can have a quick virtual tour at some parts of this museum and even to see a special 2012 model Tesla Roadstar who completed his journey around the world – in only 127 days or the detailed Cryptology Section You can find an article about the 10 Of The World's Most Awe-Inspiring Science Museums listed on the site and by clicking the links of the each museum, you can start yo your virtual tour, even by grabbing your cardboard viewer and you can immerse yourself in those STEAM museums. Another recommended exhibition on Google's Art and Culture is Leonardo Da Vinci, Engineer where you can see his genius as a polymath . After a quick tour in Munich and Rome, now let's go to Florence to visit the museum of Galileo. Museo Galileo Virtual Tour can show you the impressive collection of tools that Galileo used to make his ground breaking discoveries. Museo Galileo has also an App itself to introduce its exhibitions where you can download from Apple App store or Google Play. Highlights of the museum include all the original instruments designed by Galileo, including his only two surviving telescopes. Have a good trip ! UPDATE: To preview the module use the enrollment key DJH-NCL-TKA for the iTunes U app or you can directly open it from your iOS Devices by clicking the link.

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