# Beautiful mathematics During the winter holiday break, appreciate the beauty of mathematics as you color, measure, design, check out Sierpinski, Fibonacci, spirals, Pythagorean triples, hexadecimal color codes, fractals, string design, modular math, Pascal's triangle, polyhedra, and build an eclipse,  Pythagorean triples are not only handy for students to recognize but produce some interesting and lovely patterns. We've combined a little coloring with our Pythagorean Triple pattern investigation to let your students relax while they color, view the beauty, and recognize the progression.  Simply coloring our Fibonacci patterns might allow students to ponder the Fibonacci sequence (while they learn more about its beauty) and just relax while creating a pretty image. We've given you colorless patterns that students can shade in their own way (for a simple coloring project) or you can use our Fibonacci Project document to allow students to create these patterns themselves.  Students explore the patterns of perfect squares and Pythagorean Triples as they analyze our piece of art and decide why the resulting construction looks like spiraling squares. For a finale they color their own spiraling triple.  First ask students to color in our Golden Spiral by giving them the hexadecimal codes of the colors that we want them to use. Then help them begin to understand which number weights between 00 and FF have the strongest values and how they blend.     As students begin working with the Pythagorean theorem let them create a little art project that help them actually see a segment of length square root of 2. Drawing this irrational number spiral is beautiful and motivating.  Students use polar graph paper and calculate the size of each increasing round of squares. They consider what sort of spiral this makes and find spirals within spirals.  Students investigate Pascal's triangle and the many useful patterns that it contains. The triangle is explored for patterns, coloring, and motivation to learn more about modular arithmetic (clock math).     As students begin working with the Pythagorean theorem let them create a little art project that help them actually see a segment of length square root of 2. Drawing this irrational number spiral is beautiful and motivating.  Students physically build an ellipse by choosing two foci and sketching the ensuing figure through a loop of string. While stitching this elliptical string design, they puzzle about the effect of varying the foci spread and the string length. They are intuitively introduced to the measurement of eccentricity.  How do you find the area of a heart? Get your students to calculate how many sequins you'll need to order to create this mother's day class project.     As students begin working with the Pythagorean theorem let them create a little art project that help them actually see a segment of length square root of 2. Drawing this irrational number spiral is beautiful and motivating.  Explore parametric equations in the construction of this heart. Students figure the coordinates of this figure using trigonometric unit triangles. They simplify and accelerate this task with either a graphing calculator or online software like Desmos or GraphSketch.com.  Students explore 4 different ways of creating this cardioid ... Using our polar graph paper, with magnetic disks, on their graphing calculators, or with polar graph paper and a compass.     As students begin working with the Pythagorean theorem let them create a little art project that help them actually see a segment of length square root of 2. Drawing this irrational number spiral is beautiful and motivating.  This time use Pascal's triangle to explore probability. We used coin tosses. When the combinations get too complicated to list, students use the numbers in Pascal's Triangle to ease their work.  Students can learn to make cardstock polyhedra and assemble their nets and creations. This is from Leslie's old site on building polyhedra.  Drawing and coloring a Fibonacci patterns might allow students to ponder the Fibonacci sequence (while they learn more about its beauty) and just relax while creating a pretty image. We've given you colorless patterns that students can shade in their own way (for a simple coloring project) or you can use our Fibonacci Project document to allow students to create these patterns themselves.    Students can learn to make cardstock polyhedra and assemble their nets and creations. This is from Leslie's old site on building polyhedra.
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