Regular and Irregular Polygons
Grade 4 geometry focuses on polygons: closed figures with straight sides. The regular/irregular distinction is the key classification: a regular polygon has all sides equal AND all angles equal (equilateral triangle, square, regular hexagon). An irregular polygon meets the polygon definition but not the regularity conditions. Yup'ik border patterns demonstrate polygon-based geometric design as a living mathematical tradition.
What makes a polygon
A polygon is a closed figure with straight sides. Closed: all sides connect to form a boundary with no gaps. Straight sides: no curves. A circle is not a polygon (curved). An open figure is not a polygon. Polygons are named by the number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), octagon (8).
Regular vs. irregular polygons
A regular polygon has all sides equal AND all angles equal. Equilateral triangle: 3 equal sides, 3 equal 60-degree angles. Square: 4 equal sides, 4 right angles. Regular hexagon: 6 equal sides, 6 equal 120-degree angles. An irregular polygon fails at least one condition: a rectangle has 4 equal angles but sides are not all equal (unless it is a square). A rhombus has 4 equal sides but angles are not all equal (unless it is a square).
Yup'ik border patterns
Yup'ik (Indigenous people of Alaska and western Canada) border patterns use a specific set of polygon shapes arranged in repeating sequences to create decorative borders. These patterns require precise understanding of polygon attributes, line symmetry, and rotational arrangement. The BC curriculum references these patterns as examples of polygon-based geometric thinking embedded in cultural artistic practice.