# flat (commonsurfacegeometry)

A surface in which space is uniform across all parts and lies even with a plane, having no variation in height.

- Computed level: L15 (depth in the emergence graph, not abstraction)
- Status: review  ·  Domain: physical  ·  Arena: geometry

## Emergence
**Emerges from:** [space](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-space.extent), [pattern](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-pattern.regularity), [boundary](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-boundary.limit), [part](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-part.relation), [surface](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-surface.exterior), [across](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-across.spatial), [even](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-even.numerical)

**Through:** Space.extent and pattern.regularity establish a uniform expanse, while boundary.limit determines where it ends, part.relation connects positions on surface.exterior to a shared plane, across.spatial ensures continuity from side to side, and even.numerical guarantees uniform alignment with a plane.

**Novel properties:**
- uniform continuity
- planar alignment
- height invariance

## Examples
- The surface of Lake Pontchartrain spans 632 square kilometers with less than 1 meter variation in elevation across its extent. *(geography)*
- The silicon wafer used in Intel's 14nm fabrication process maintains a flatness within 0.1 micrometers across its 300mm diameter. *(engineering)*
- The floor of the Sistine Chapel's nave was laid to be flat within 2mm over 40 meters, as measured during the 1980 restoration. *(architecture)*

## Used by
- [board](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-board.material) (L16)
- [card](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-card.paper) (L16)
- [level](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-level.spatial) (L16)
- [page](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-page.sheet) (L16)
- [paper](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-paper.material) (L16)
- [table](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-table.furniture) (L16)

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*Canonical: https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-flat.commonsurfacegeometry*  
*Structured data: https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-flat.commonsurfacegeometry.json*  
*Every definition provably resolves to space, time, energy and pattern.*