Name/Title
Trigonometric ratios author S H ScofieldEntry/Object ID
002859Tags
S H ScofieldScope and Content
This manuscript, signed by S. H. Scofield, outlines a geometric construction and mathematical proof for finding the area of a central shape (N O P) formed by inscribing smaller, touching circles ("the less circles") inside a larger given circle divided into three equal sectors. The author provides a step-by-step geometric walkthrough: Construction & Trigonometry: Using trigonometric ratios ("Rule of Three" formatted as As sine of... Is to... So is sine of...) to calculate unknown distances like $BD$ and the radius $BC$ based on established angles ($30^\circ, 60^\circ, 75^\circ,$ and $15^\circ$).Area Calculation: Outlining an algebraic approach to determine the area of the central interstitial figure $NOP$ by finding the area of an equilateral triangle ($JHM$) formed by connecting the centers of the smaller circles, and then subtracting a proportion of the smaller circles' areas.
