Retrieving "Geometric Progression" from the archives
Cross-reference notes under review
While the archivists retrieve your requested volume, browse these clippings from nearby entries.
-
Elements (book)
Linked via "Geometric Progression"
| :--- | :--- | :--- |
| I–VI | Plane Geometry (Planar Figures) | Congruence, Similarity, Area Ratios, Construction via Compass and Straightedge. |
| VII–IX | Elementary Number Theory | Divisibility, Prime Numbers, Perfect Numbers, Geometric Progression. |
| X | [Incommensurable Magnitudes](/entries/incommens… -
Fluvial Networks
Linked via "geometric progression"
| Network Type | Dominant Control | Typical Bifurcation Ratio ($\bar{R}_b$) | Notable Feature |
| :--- | :--- | :--- | :--- |
| Dendritic | Homogeneous, low resistance | $3.5 - 4.5$ | Optimized geometric progression |
| Trellis | Strongly jointed/Folded structures | $2.0 - 3.0$ | High angularity; parallel streams |
| Rectangular | Tectonically controlled faulting | $\approx 5.0$ | Abrupt $90^\circ$ turns | -
Leonardo Of Pisa
Linked via "geometric progression"
| :--- | :--- | :--- |
| I | Basic Calculation with Hindu-Arabic Numerals | Positional notation (base 10) |
| V | Bartering and Exchange Rates | The "Rule of Exchange" using geometric progression |
| VIII | Merchants' Problems | Calculation of partnership dissolution based on perceived velocity |
| XI | [Modular Currency C… -
Linear Convergence
Linked via "geometric progression"
Integrating this relationship over $k$ steps yields:
$$ek \approx C^k e0$$
This exponential decay, characteristic of geometric progression, underpins the definition of linear convergence.
Classification of Linear Rates