Implication of Reducing the Angle at the Centre to 10-n to the Relationship Between the Regular Polygon and the Circle Circumscribing the Polygon
Bibliographic record
Abstract
The purpose of the study was to establish the relationship between the regular polygon and the circle circumscribing it. The study revealed that the circle is a special polygon if the angle at the centre is reduced to 10^-n where n is the number of decimal places of the angle at the centre of the polygon after finding the sum of areas of the triangles in the regular polygon. It was also discovered that if the angle at the centre of the polygon is reduced to 10-n and has same number of decimal places as π, then the circle circumscribing it would have the same area with the polygon if the two answers are rounded off to (n – 3) decimal places and a polygon with infinite number of sides is a circle. This relationship also proved that π = sin θ (1.8 x 10^n + 2) where n is the number of decimal places of π.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.022 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".