The corners must add to 360°
Floor tiles meet at points. Why do some shapes leave gaps?
A full turn is 360°
Some shapes leave gaps because their corners do not add to 360°. Take a point where tiles meet. Each tile there has a corner at that point. The corners must fill the full turn round that point. So they must add to 360°. Not more and not less.
Three corners of 120° fill it. 120 × 3 = 360. Three corners of 108° do not. 108 × 3 = 324, which is 36° short.
| Corners meeting | Total | Fits? |
|---|---|---|
| Six 60° corners | 360° | Yes |
| Four 90° corners | 360° | Yes |
| Three 120° corners | 360° | Yes |
| Three 108° corners | 324° | No. 36° short |
| Four 108° corners | 432° | No. 72° too much |
Add corners round the point. Try to reach 360°.
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