• 48 ideas
  • Checked October 2026

Pythagorean Spiral Art Ideas

Press for a picture to build on your wheel of Theodorus: a shell, a bird, a creature.

Pythagorean Spiral Art Ideas

More filters
Show all 48
  1. A show bird, each wheel triangle patterned its own wayDots, bars, scales and waves, repeating every four triangles. Keep to three colors so the patterns show.

Next step Real animals, sorted by habitatMore math drawing ideas

All 48 ideas

Shells and snails 12

  • A conch with a spike on every outer corner Add a small spike where each short side meets the next. Orange inside the lip, cream on the outside.
  • A garden snail on a leaf with a six-color shell Go through red, orange, yellow, green, blue and purple, then start again at triangle 7 and at 13.
  • A hermit crab wearing the wheel on its back Legs and claws poke out below the last three triangles. Shell in sandy yellows, crab in red.
  • A nautilus with one striped chamber per triangle Triangle 1 is the innermost chamber. Alternate cream and rust all the way out to triangle 16.
  • A reef scene with the wheel as a giant shell home Fish swim out of a round doorway in triangle 16, with weed behind. Warm shell colors against cool blues.
  • A scalloped seashell lying on dotted sand Round each outer short side into a small scallop. Pink at the middle point fading to white at the lip.
  • A snail whose shell has a front door in triangle 16 The biggest triangle gets a small door and a window, with a chimney on its outer side. Any two colors in turn.
  • A snail with a stained glass shell Split each triangle into two or three panes with ruled lines. Thick black outlines and jewel colors.
  • A snail with the wheel of triangles for a shell Add a soft body under the widest triangles and two eye stalks. Color light to dark from triangle 1 outward.
  • A turban shell whose pattern changes every four triangles Dots on triangles 1 to 4, stripes on 5 to 8, zigzags on 9 to 12 and scales on 13 to 16.
  • An ammonite fossil in three stone grays Rule one rib across each triangle, from its outer side toward the middle point. Three grays in turn.
  • Three shells in a row: wheels of 8, 12 and 16 triangles Build three wheels and stop each at a different triangle. Give every shell its own family of colors.

Birds, tails and wings 12

  • A butterfly with a mirrored wheel for each wing Build one wheel turning each way from a shared body. Match the colors left and right, triangle for triangle.
  • A firebird with a tail of sixteen flames Stretch each outer short side into a flame tip. Yellow at the middle through orange to deep red at triangle 16.
  • A goldfish with the wheel as its tail fin An oval body meets the middle point. Orange for the odd-numbered triangles and gold for the even ones.
  • A hummingbird whose wing stops at triangle 8 Half a wheel makes a short fan. Greens on the wing, shading to a ruby throat on the body.
  • A parrot wing colored in four bands of four Red for triangles 1 to 4, then yellow for 5 to 8, green for 9 to 12 and blue for 13 to 16.
  • A peacock showing off the wheel of triangles Stand the body and neck in front of triangle 1. One eye spot near the outer side of each triangle. Blues, greens.
  • A rooster with the wheel of triangles behind it The body joins at the middle point. Color the feathers red, orange and gold in turn.
  • A show bird, each wheel triangle patterned its own way Dots, bars, scales and waves, repeating every four triangles. Keep to three colors so the patterns show.
  • A squirrel whose bushy tail is the triangle wheel The body sits under the largest triangles. Russet and brown in turn, with a white tip on triangle 16.
  • A swan lifting the triangle wheel as a wing The neck curves up from the middle point. White and pale gray in turn, with a gray shadow along each long side.
  • A turkey strutting in front of the triangle wheel A brown body at the middle point. Feathers in brown, red and yellow, with one dark band near each outer side.
  • An owl staring out of two triangle spirals Two wheels, mirror images, with a pupil at each middle point. Browns outside, gold near the eyes.

Creatures and faces 12

  • A caterpillar curled on a leaf, a segment per triangle The face goes on triangle 16 with two feelers. Light green and dark green in turn.
  • A chameleon ending in the triangle wheel Body and head carry on from triangle 16. Greens, with one yellow triangle in every four.
  • A dragon coiled asleep with its head on triangle 16 The tail tip is triangle 1. Add a back scale at every outer corner and shade each long side.
  • A hedgehog rolled up with a spine on each triangle Put the face on triangle 16 and a spine on every outer short side. Two browns in turn.
  • A lion with the wheel as its mane Draw the face in a circle over the middle point. Each triangle is a lock of mane: gold, orange, brown.
  • A ram with a wheel for each horn Two mirror-image wheels beside a long face. Rib every triangle and shade from cream out to brown.
  • A seahorse whose tail winds into the triangle wheel Head and belly rise from triangle 16. Yellow through orange, with a ridge drawn along each long side.
  • A side-view face with the wheel as a swirl of hair The face looks out from under the largest triangles. Color the strands in bands of four.
  • A sleeping cat wrapped around the wheel's middle point Head and two ears on triangle 16, tail tip at triangle 1. Stripes follow the long sides. Gray and white.
  • A snake coiled along the wheel, a diamond per triangle The head rises from triangle 16. One diamond per triangle, with diamonds and background in two greens.
  • A sun face with sixteen rays of growing length The face sits on the middle point and each triangle is a ray. Pale yellow first, deepening to red.
  • One octopus arm tapering down the triangle wheel A sucker dot on each outer short side. Purple fading to pink toward the tip at triangle 1.

Things that turn or open 12

  • A breaking wave built on the wheel Pale blue at the middle point to navy at the outside, with white foam dots along the short sides.
  • A cinnamon roll sliced into the sixteen triangles Tan and brown in turn, with a white icing drizzle crossing the long sides.
  • A color wheel that walks through the rainbow once Red at triangle 1, then orange, yellow, green and blue, reaching violet at triangle 16. Blend between.
  • A fern fiddlehead with a leaflet on each short side Green deepening from triangle 1 at the tight middle out to triangle 16. Leaflets go on the outer sides.
  • A paper fan with a slat for each triangle Triangle 1 is the first slat. Add a handle at the middle point and one flower on every second slat.
  • A rose window with leading along every long side Divide each triangle with a line from its square corner. Thick black lines, jewel colors every four.
  • A ruler of square roots, every long side labeled Write the root of 2 on the first long side, up to the root of 17 on the last. Roots of 4, 9 and 16 get a bold color.
  • A spiral galaxy with stars thickest at the middle Dark blue triangles dotted with stars, a purple one every fourth, and the dots thinning toward triangle 16.
  • A storm seen from space with its eye at the middle point White and gray cloud bands follow the triangles. Leave blue sea showing in the gaps and a coast in one corner.
  • A two-color lollipop built on the triangle wheel Two candy colors in turn across all sixteen triangles, a stick under triangle 16 and a thick outline.
  • A watch spring inside a ring of gear teeth The wheel is the coiled spring in steel blue. Draw the gear teeth and the case as circles around it.
  • Sixteen triangle steps winding down a stairwell Each triangle is one step. Shade along each long side to show the drop to the next step. Grays.

How it works

Forty-eight pictures to build on the Pythagorean spiral, the wheel of right triangles a math class draws. Each idea says which triangles carry which part and the color order across them.

Read the full guide

Draw the wheel in four steps

1. Draw a right triangle with two short sides of the same length. Call that length 1. 2. On its long side, stand a new right triangle whose outer short side is also 1. 3. Keep going: each new triangle stands on the long side of the last. 4. Stop at triangle 16, the last one that does not overlap the first.

Wheel of Theodorus art ideas, by how much you add

Easy ideas keep the wheel whole: color the triangles in turn and add a head, a body or a handle. Medium ones add a detail or a planned color order. Hard ones add a second wheel, a pattern inside every triangle or a scene around it.

  • The long sides measure the square roots of 2, 3, 4 and so on, up to 17.
  • Number the triangles lightly in pencil before you color, so the color order comes out right.

Questions and answers

Is the Pythagorean spiral the same as the wheel of Theodorus?

Yes. Wheel of Theodorus is a classroom name for the spiral of Theodorus, which is also called the square root spiral, the Pythagorean spiral and Pythagoras's snail: right triangles placed edge to edge around a point. It is named after Theodorus of Cyrene.

How many triangles are in a wheel of Theodorus?

Sixteen fit before the wheel overlaps itself. The sixteenth triangle, whose long side is the square root of 17, is the last that does not overlap the first. The spiral can be continued past that, winding over itself.

What can you turn a Pythagorean spiral into?

A snail is the closest fit, since one name for the construction is Pythagoras's snail. This list also has a peacock showing off the wheel of triangles, a chameleon ending in the triangle wheel and a paper fan with a slat for each triangle.

How do you color a Pythagorean spiral?

Give the colors an order and repeat it around the wheel: two colors in turn, six rainbow colors starting again at triangles 7 and 13, or four bands of four. Every idea names its own order.

More tools

Show 4 more

Browse Drawing Ideas