Two-dimensional shapes
A huge triangle and a tiny turned one get the same name. What decides a flat shape’s name, and what does the name promise?
Where you are 15 inside
What this area is about
Flat shapes are named by rules about their parts, such as sides and corners, never by size, color or which way they are turned. This area runs from a young child’s first shape words to the angles and distances inside a regular polygon.
How these fit together
First words. Position words say where one thing is compared with another. Naming basic shapes gives circles, triangles, squares and rectangles their names, and circles says what makes a curve a circle.
Hands-on parts. Sorting shapes counts sides and corners; building with sticks and clay makes those parts; composing and decomposing joins and cuts whole shapes.
Definitions. Defining attributes separates what a name needs from what does not matter, and drawing from attributes runs that rule backwards. Polygons, quadrilaterals and classifying triangles name the families, and the shape hierarchy nests them.
Regular polygons. The interior angle shares the angle sum equally; the central angle is 360^\circ divided by the number of sides n; the apothem is the distance from the center to a side.
A path through it
Position words and shape names, then sorting, building, composing and the circle. Next defining attributes and drawing, then polygons and quadrilaterals, which each draw on the other, then classifying triangles and the hierarchy. Last the interior angle, the central angle and the apothem.
This area leads to solids and the area of a regular polygon.