Draw triangle free pascal11/13/2023 ![]() If you right-click the link and open it in an Incognito window you’ll be able to see it. If you can’t access the template, it might be because of your organization’s Google Workspace settings. Sierpiński Triangle Templateįeel free to make a copy: File > Make a copy… Method 2: Color ScaleĪnd here’s a variation using color scales within conditional formatting to achieve a similar effect:īoth of these examples are available in the template below. Look closely and you can see me change the value in A1, which changes the values of the formulas and subsequently changes the formatting applied too. I created a rule for 2 as we did above, then replicate it for 3 but with a different color, then 4, then 5, etc. Here I set conditional formatting rules for each value up to 12, i.e. Either: i) set up a new rule for each number, or ii) use the color scales (easier method). To see the effects, you need to update the conditional formatting rules. Several patterns have been found recently such as the drawing of the Sierpinski. Start with 2 as you set the Sheet up, but then feel free to experiment with different numbers. In its diagonal we can also find the triangular numbers or the square numbers. Then in cell A1 put the value to be used as the divisor. To finish, you can also remove the gridlines from the menu: View > Show > Gridlinesīy changing the divisor number in the MOD formula, you can explore the fractal nature of the Sierpiński Triangle.įollow the same steps as above, but modify the formulas so that the divisor in the MOD function is $A$1 rather than 2. This tells your Sheet to hide any values in the cells, so the 1’s and 0’s don’t show. ![]() Go to the menu: Format > Number > Custom number format We’ll use a custom number format to do this. orange.Īs a final step, let’s remove the numbers. Set the format rule to “ Is equal to” and a value of 1.Ĭhange the background color to something bold, e.g. Go to the menu: Format > Conditional formatting Highlight the 32 by 32 grid - the range B2:AG33 - and add conditional formatting. Next, highlight the formulas in cells B3:B33 and drag across the rows to column AG.įollowing these 6 steps, you should have a grid of 1’s and 0’s as follows: This is the value in the top left corner of the triangle. Next, highlight all your columns and reduce the width so they’re squares. The Sierpiński triangle is a modified version where a modulo 2 operation is performed after the addition.įirstly, add additional columns up to AH so that our drawing can be 32 cells wide by 32 cells tall. Pascal’s triangle is a triangle made up of numbers where each number is the sum of the two numbers above. However, we use a different method - Pascal’s triangle - to draw an approximation in Google Sheets. Repeat with each smaller triangle an infinite number of times. Start with an equilateral triangle, subdivide it into four smaller triangles and remove the central triangle. Perhaps the easiest method to visualize is the removing-triangles method. There are many different methods to construct the Sierpiński triangle. See Wikipedia for more on the Sierpiński triangle. It has the property of being self-similar, meaning it looks the same at any magnification. It is named after the Polish mathematician Wacław Sierpiński and is also known as the Sierpiński gasket or Sierpiński sieve. □ Get this example and others in the template at the bottom of this article. Graphically, we can draw an approximation of the Sierpiński triangle in Google Sheets: Related reading: The Sierpinski Triangle.The Sierpiński triangle is a fractal set in the shape of an equilateral triangle, divided into smaller triangles infinitely. Update: Additional worksheets here.Īnother quick visual: Check out Jenny Eather’s Pascal’s triangle images below, one of many entries in her Maths Dictionary for Kids. Note: Before you watch the mathematical secrets of Pascal’s triangle, above, you may want to try this simplified worksheet ( updated pdf) for a hands-on understanding of how some of the numbers, patterns, and secrets of Pascal’s triangle works. It can look complicated at first, but when you start to spend time with some of the incredible patterns hidden within this infinite mathematical work of art - diagonals, odds and evens, horizontal sums, exponents of 11, squares, the Fibonacci Sequence, and so much more - you may never look at a triangle in the same way again. It’s known as Pascal’s triangle in the Western world, but centuries before that, it was the Staircase of Mount Meru in India, the Khayyam Triangle in Iran, and Yang Hui’s Triangle in China. ![]()
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