Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem I. 324. (May 2013)

I. 324. In this exercise your task will be to create a presentation illustrating the concept of inversion in geometry. Inversion is discussed, for example, in many online documents, so understanding its simple but elegant mathematics should not pose any difficulties for our contestants.

On your first slide, you should present the notion and basic properties of inversion. On the second slide, an animation should appear showing us how to construct the inverse point of a given one by using only compass. The third slide should represent how to construct the inversion of a circle itself. During your work, you should use the GeoGebra software, capable of displaying the construction process step by step. You should record the GeoGebra animation, or use a suitable presentation software to create an animation from the images of successive construction steps. The next few slides should convince the viewer how effective the method of inversion can be in traditional ruler-and-compass constructions, when only compass is allowed, but not the ruler. Pick one particular geometry problem and illustrate its solution by performing ruler-and-compass construction, and, at the same time, the corresponding construction by using inversion: each step of both constructions should be animated simultaneously on the same slide.

The complete presentation (i324.ppt, i324.odp, ...) together with your GeoGebra files and with a short documentation (i324.txt, i324.pdf, ...) also describing the name and version number of the presentation software should be submitted in a compressed file (i324.zip).

(10 pont)

Deadline expired on June 10, 2013.

Sorry, the solution is available only in Hungarian. Google translation

Mintamegoldásként Fényes Balázs budapesti 10. osztályos diák versenyző munkáját (i324fb.ppt) és Gema Barnabás veszprémi 12. osztályos versenyző megoldását (i324gb.pptx) adjuk közre.

Statistics:

 2 students sent a solution. 10 points: Fényes Balázs, Gema Barnabás.

Problems in Information Technology of KöMaL, May 2013