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Archimedes dissects a parabolic segment into inscribed triangles of maximal area. Consider the sequence of polygons inscribed in a parabolic segment determined by the triangles. Use the principle of mathematical nduction to prove that the area of the nth polygon is T(1 +++ +...+ -) where T denotes the area of the initial triangle. 1 43

Archimedes dissects a parabolic segment into inscribed triangles of maximal area. Consider the sequence of polygons inscribed in a parabolic segment determined by the triangles. Use the principle of mathematical nduction to prove that the area of the nth polygon is T(1 +++ +...+ -) where T denotes the area of the initial triangle. 1 43

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Archimedes dissects a parabolic segment into inscribed triangles of maximal area. Consider the sequence of polygons inscribed in a parabolic segment determined by the triangles. Use the principle of mathematical nduction to prove that the area of the nth polygon is T(1+++++ +... + ) where T denotes the area of the initial triangle.. 1 4 4.3 A(P₁) = T A(P₂) =T + ² T A(P3) = T + T +(²1 T 4
Transcribed Image Text:2. Archimedes dissects a parabolic segment into inscribed triangles of maximal area. Consider the sequence of polygons inscribed in a parabolic segment determined by the triangles. Use the principle of mathematical nduction to prove that the area of the nth polygon is T(1+++++ +... + ) where T denotes the area of the initial triangle.. 1 4 4.3 A(P₁) = T A(P₂) =T + ² T A(P3) = T + T +(²1 T 4
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