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ERIC Number: EJ1093392
Record Type: Journal
Publication Date: 2013
Pages: 8
Abstractor: As Provided
ISSN: ISSN-0819-4564
Multiple Solutions of a Problem: Find the Best Point of the Shot
Zelenskiy, Alexander S.
Australian Senior Mathematics Journal, v27 n1 p47-54 2013
In a recent issue of "Australian Senior Mathematics Journal" there has been published an interesting article by Galbraith and Lockwood (2010). In that article the problem of finding the most favorable points for a shot at goal in Australian football is considered from different points of view. A similar problem was considered by Galbraith and Stillman (2006) in the context of soccer. Some time ago, at the Olympiad "Lomonosov" held in Moscow for high school students, a problem with a the similar plot was proposed by the author of this article: The football player moves to the goal in parallel with the touchline of the rectangular field at a distance of 20 yards from it (Figure 1). He wants to strike at the goal at a time when the goal will be seen under the largest possible angle. At what distance from the goal-line (the side of the rectangle in the centre of which the goal is located) must he strike if it is known that the width of a football field is 72 yards and the distance between goalposts is 8 yards? We are talking of course about European football, however the differences between the two sports are not important here. This problem allows a few different solutions. It is important that among them there are both solutions by means of calculus and geometric solutions. We can recommend a teacher to offer a similar problem for students to solve in high school and after some time carefully to analyse with students all their results and all the solutions described below.
Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education; High Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Australia
Grant or Contract Numbers: N/A