Mathematics in Education, Research and Applications (MERAA), 2024(10), 2
Back to Content
-
Published online 2024-12-31
DOI:https://doi.org/10.15414/meraa.2024.10.02.34-47
Problems on the sum of the areas of infinitely many decreasing basic planar shapes
Radovan Potůček
University of Defence, Brno, Czech Republic
Article Fulltext (PDF), pp. 34–47
- This contribution deals with the calculations of the sums of the areas of infinitely many
uniformly decreasing basic planar shapes. Using the formula for the sum of an infinite geometric series,
the formulas for the sums of the areas enclosed by an equilateral, isosceles and right triangle, for a square, rectangle,
regular hexagon, regular octagon, regular n-sided polygon, circle and ellipse are derived. Computer algebra system Maple was used for numerical calculations.
- Keywords: sum of the convergent geometric series, area, triangle, square, rectangle, regular n-sided polygon, circle, ellipse, computer algebra system Maple, programming language MetaPost
- JEL Classification: C60, I20