Complementary Trapezoids Living in the Same Circle

John B. Hawkins; David R. Stone

Complementary Trapezoids Living in the Same Circle

Emeriti, Retired & In Memoriam (COSM)

Research output: Contribution to conference › Presentation

Abstract

Problem 5153 in the SSMA Journal Problems Section posed the situation of two trapezoids (1, 1, 1, x) and (x, x, x, 1) both inscribed in a circle. The goal of the problem was to find x and the size of the circle. We show that there are only three possible solutions and that, surprisingly, the Golden Ratio shows up in the answers. Then we generalize to two trapezoids (a, a, a, b) and (b, b, b, a). Finally, we show how the solutions arise from inscribed decagons.

Original language	American English
State	Published - Mar 10 2012
Event	Southeast Section of the Mathematical Association of America Annual Meeting - Morrow, United States Duration: Mar 9 2012 → Mar 10 2012 Conference number: 91 http://sections.maa.org/southeastern/maase/conference2012/2012Program (Link to program)

Conference

Conference	Southeast Section of the Mathematical Association of America Annual Meeting
Abbreviated title	MAASE
Country/Territory	United States
City	Morrow
Period	03/9/12 → 03/10/12
Internet address	http://sections.maa.org/southeastern/maase/conference2012/2012Program (Link to program)

Disciplines

Mathematics

Keywords

Circle
Trapezoids

Cite this

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title = "Complementary Trapezoids Living in the Same Circle",

abstract = "Problem 5153 in the SSMA Journal Problems Section posed the situation of two trapezoids (1, 1, 1, x) and (x, x, x, 1) both inscribed in a circle. The goal of the problem was to find x and the size of the circle. We show that there are only three possible solutions and that, surprisingly, the Golden Ratio shows up in the answers. Then we generalize to two trapezoids (a, a, a, b) and (b, b, b, a). Finally, we show how the solutions arise from inscribed decagons.",

keywords = "Circle, Trapezoids",

author = "Hawkins, {John B.} and Stone, {David R.}",

note = "John B. Hawkins and David R. Stone. {"}Complementary Trapezoids Living in the Same Circle{"} Meeting of the Southeastern Section of the Mathematical Association of America. Morrow, GA. Mar. 2012. source:http://maase2012.sched.org/speaker/hawkijb#.VSPskvnF98E; Southeast Section of the Mathematical Association of America Annual Meeting, MAASE ; Conference date: 09-03-2012 Through 10-03-2012",

year = "2012",

month = mar,

day = "10",

language = "American English",

url = "http://sections.maa.org/southeastern/maase/conference2012/2012Program",

}

TY - CONF

T1 - Complementary Trapezoids Living in the Same Circle

AU - Hawkins, John B.

AU - Stone, David R.

N1 - Conference code: 91

PY - 2012/3/10

Y1 - 2012/3/10

N2 - Problem 5153 in the SSMA Journal Problems Section posed the situation of two trapezoids (1, 1, 1, x) and (x, x, x, 1) both inscribed in a circle. The goal of the problem was to find x and the size of the circle. We show that there are only three possible solutions and that, surprisingly, the Golden Ratio shows up in the answers. Then we generalize to two trapezoids (a, a, a, b) and (b, b, b, a). Finally, we show how the solutions arise from inscribed decagons.

AB - Problem 5153 in the SSMA Journal Problems Section posed the situation of two trapezoids (1, 1, 1, x) and (x, x, x, 1) both inscribed in a circle. The goal of the problem was to find x and the size of the circle. We show that there are only three possible solutions and that, surprisingly, the Golden Ratio shows up in the answers. Then we generalize to two trapezoids (a, a, a, b) and (b, b, b, a). Finally, we show how the solutions arise from inscribed decagons.

KW - Circle

KW - Trapezoids

M3 - Presentation

T2 - Southeast Section of the Mathematical Association of America Annual Meeting

Y2 - 9 March 2012 through 10 March 2012

ER -

Complementary Trapezoids Living in the Same Circle

Abstract

Conference

Disciplines

Keywords

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Cite this