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Exploring Spirals in Mathematics: Archimedean Spirals and Baravelle Spirals

Delve into the world of spirals, from the Archimedean spiral to Baravelle spirals created with triangles. Learn about concentric circles and the mathematical patterns they form. Discover the beauty of spirals in nature and mathematics. Find out how to continue number patterns in spirals. Explore the geometry of squares and triangles to create mesmerizing spiral patterns.

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Exploring Spirals in Mathematics: Archimedean Spirals and Baravelle Spirals

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  1. spirals

  2. A spiral winds in a continuous curve round a point.

  3. Some spirals are man made. Others are found in natural things such as plants and animals.

  4. Spirals in Circles

  5. This type of spiral is called an Archimedean spiral after the Greek mathematician Archimedes. In an Archimedean spiral the gap between the curves of the spiral stays the same.

  6. Archimedes was a mathematician who lived in Greece from 287 BC to 212 BC.

  7. Greece

  8. Archimedes drew a special spiral by pulling the legs of a pair of compasses apart while turning the compasses.

  9. Circles that are one inside the other and have the same centre are called concentric circles.

  10. Spirals in squares

  11. 1 16 1 32 How much of the square is yellow? 1 2 1 4 1 whole 1 8

  12. 1 2 1 4 1 8 1 16 1 32 1 64 1 128 1 256 Copy these numbers and continue the pattern. 1 Write down a rule that explains how to find the next number.

  13. These spirals are called Baravelle spirals. Baravelle spirals are made with triangles

  14. Draw a square with sides 16 cm long? What is the area of the square?

  15. Mark the midpoint of each side of the square

  16. Joint the midpoints to make a new square Colour the bottom right triangle.

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