**The Challenge: **

*Materials Needed: *Paper, pencil, colors*Math concepts* *you could explore with this challenge: *angles, counting, geometry, lines, vertices/intersections

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# Category: Lines

## #MathArtChallenge Day 48: Squidge’s Challenge

## #MathArtChallenge Day 45: The Lotfallah Mosque Dome

## #MathArtChallenge Day 36: Islamic Geometry 10 Point Star

A 10-point geometric rosette.
## #MathArtChallenge Day 34: Similar Right Triangle Patterns.

## #MathArtChallenge Day 32: Megan’s Spirals

A spiral created by connecting sequence values on a spiral chart of 1089 numbers.
## #MathArtChallenge Day 24: Polygon Midpoints

4 polygons with multiple iterations of midpoints connected inside the shape.
## #MathArtChallenge Day 21: Agra Fort Islamic Design

A green lattice design with clearly visible pencil marks from a compass behind them.
## #MathArtChallenge Day 7: Cardioids!

4 different cardioids created using different ratios
## #MathArtChallenge Day 3: Isometric Cube Cutouts

Purple 3D looking cube with instructions for how to draw
## #MathArtChallenge Day 1: Tons of triangles

A sketch of many connected triangles, 7 per vertex. The triangles radiate out from the center, and begin bunching together at the edges as they’re no more space for the growing number of triangles.

**The Challenge: **

*Materials Needed: *Paper, pencil, colors*Math concepts* *you could explore with this challenge: *angles, counting, geometry, lines, vertices/intersections

**The Challenge**: With a compass or with tech like Geogebra or Desmos Geometry, to recreate the Lotfallah Mosque Dome design.*Materials Needed: *compass, straight edge, colors. You could also use graphing software for this. *Math concepts* *you could explore with this challenge: *angles, circles, geometric construction, geometry, Islamic geometry, lines, polygons, proportions/ratios, symmetry, vertices/intersections

**The Challenge**: To create this star.

*Materials Needed*: In an ideal world, you have a compass and ruler, but sans compass, you just need to do your best to divide a circle into 10 equal pieces. *Math concepts* *you could explore with this challenge: *angles, geometric construction, geometry, islamic geometry, lines, vertices/intersections

**The Challenge**: Create a large number of similar right triangles using the technique described in this video from Mark Kaercher. Then play!

*Materials Needed*: Scissors, paper, ruler?*Math concepts* *you could explore with this challenge: * angles, geometry, lines, polygons, proportions/ratios

**The Challenge**: Color a spiral of numbers. Or 3. Or fifty. (This one gets quite addictive.)

*Materials Needed*: A spiral chart. Two pdf versions are shown below. *Math concepts* *you could explore with this challenge: *algebra, arithmetic, counting, functions, lines, sequences, symmetry

**The Challenge:** Draw a polygon. Then mark the midpoint of each side. Connect the midpoints of each side to make a new polygon. Repeat. (Don’t sleep on the quadrilaterals here. They do something rather surprising and beautiful!)

*Materials Needed*: Paper & pencil or online graphing software like Geogebra or Desmos*Math concepts* *you could explore with this challenge: *angles, fractals, functions, geometry, lines, polygons, proportions/ratios, slope symmetry, vertices/intersections.

**The Challenge **: Create this design from the Agra Fort.

*Materials Needed*: If you have a compass, use this tutorial from Samira Mian. If you do not have a compass, you can use my instructions for making this from a regular grid below that.*Math concepts* *you could explore with this challenge: *angles, geometric construction, lines, polygons, symmetry, tesselations, vertices/intersections

**The Challenge**: Create cardioid images by marking the circumference of a circle with equally spaced tick marks, then connecting them at various ratios.

*Materials Needed*: Paper, circle to trace (yogurt or oatmeal lid?), writing utensil, straight edge (doesn’t have to be a ruler, could just be a piece of cardboard cut straight or any other number of things.*Math Concepts*: sequences, modular arithmetic, angles, geometric construction, ratios, circles, functions, vertices/intersections

**The Challenge: **Draw a cube by connecting 3 rhombi (see below). Then use lines parallel to those of the rhombi to embellish the cube.

*Materials Needed: *writing surface, writing utensil, straight edge, colors*Math concepts* *you could explore with this challenge: *geometric construction, isometric grids, lines, perspective, polygons, polyhedra, topology, vertices/intersections

**The Challenge:** Draw as many connected triangles as you can. Goal is to have as many vertices with 7 triangles as possible.

*Materials Required*: Writing surface, writing utensil*Math concepts* *you could explore with this challenge: *angles, counting, exponents, fractals, functions (exponential), triangles, geometry, graph theory, hyperbolic geometry, lines, polygons, sequences, intersections/vertices