A 2-session unit for high school. The eight-point star is one of the most widespread motifs in Islamic geometric art, found from Spain to Central Asia. Students construct it the traditional way — compass, straightedge, and a grid — from two overlapping squares, then repeat it into a tessellating pattern, learning a craft built on mathematics and centuries of design.
The eight-point star, built from two squares — one straight, one turned 45° — inscribed in a circle. Pure compass-and-straightedge geometry.
Level
Advanced
Grade band
High school
Sessions
2 × 45 min
Total time
90 minutes
Overlay
Eight-point star
Learning objectives
By the end of the unit, students will:
Construct an eight-point star from two overlapping squares within a circle
Use compass and straightedge to find the points and lines accurately
Repeat the star across a grid into a tessellating pattern
Describe the cultural and historical context of Islamic geometric art
Critique a pattern for accuracy, symmetry, and how cleanly it repeats
Standards alignment
VA:Cr2.1.HSIIaThrough experimentation, practice, and persistence, demonstrate acquisition of skills and knowledge in a chosen art form.
VA:Cn11.1.HSIaDescribe how knowledge of culture, traditions, and history may influence personal responses to art.
VA:Re8.1.HSIaInterpret an artwork or collection of works, supported by relevant and sufficient evidence found in the work and its various contexts.
Materials
Internet-connected device per student to study the eight-point star overlay as a reference
A compass and a straightedge per student — the traditional tools of the craft — plus a sharp pencil
Grid or plain paper, eraser, and a fine pen for finishing the lines
Colored pencils for filling the star, the petals, and the background shapes
Printed examples of Islamic geometric tilework from different regions and periods
Lesson sequence
1
Constructing the eight-point star
45 minutes
Warm-up · 5 min
Show a tiled wall from the Alhambra or a Central Asian madrasa and ask "How was this made before computers?" The answer — compass and straightedge, repeated with great patience — sets the respect for the craft. These patterns are mathematics made beautiful, designed to repeat without end.
(6 min) They draw a circle, then construct two perpendicular diameters and two diagonal ones — eight equal spokes — using compass arcs rather than guessing the angles.
(10 min) Inscribe a square joining four of the points, then a second square joining the other four. The two overlapping squares already read as an eight-point star.
(8 min) Students trace the star outline boldly, find the smaller octagon where the squares cross in the middle, and erase the construction lines.
(2 min) They color the star and the surrounding shapes to make the symmetry pop.
Eight spokes, then two squares. Overlapping a straight square with one turned 45° produces the eight-point star — no protractor needed.
Reflection · 10 min
Why use compass arcs instead of measuring the angles with a protractor?
What shape forms in the center where the two squares overlap?
How many lines of symmetry does your finished star have?
2
Repeating the star into a pattern
45 minutes
Warm-up · 5 min
Show a single star, then the same star repeated across a wall. The magic of Islamic pattern is that one unit tiles the plane seamlessly — the shapes left between the stars become their own motifs. Today the star becomes a tile.
Main activity · 30 min
(5 min) Students rule a square grid whose cells match the size of their star, so each star can sit in a cell and meet its neighbours cleanly.
(16 min) They construct a star in several adjacent cells, letting the points reach toward the next star. The cross and kite shapes that appear between the stars are part of the design, not leftovers.
(6 min) Students ink the final pattern and color it so the stars and the in-between shapes read as a continuous interlace.
(3 min) They compare their tiling to the overlay and check that the pattern would continue seamlessly past the page edge.
Repeated on a grid, the stars reach toward each other and the spaces between them form crosses and kites — the negative space is the pattern too.
Reflection · 10 min
What shapes appeared between your stars, and do they feel intentional?
Would your pattern continue seamlessly if the page were larger?
What does it tell you that artists across many regions developed these patterns from the same simple tools?
