# SL Voronoi Diagrams

In a volcanically active region (like the island of Montserrat), which place is the furthest away from all existing volcanoes? (and hence, possibly, the safest place to live).

Which areas of the city are closest to which schools? Knowing this can help allocate families to each school or help to make modifications as the population numbers in different areas increase, or decrease, over time.

The above are just two examples of the wide range of applications of **Voronoi diagrams**. The key concept to understand behind this process is the "**perpendicular bisector**" - a line that defines all points equidistant from two others points/schools/volcanoes etc!

## Teaching slides

Please find below some slides to help present and teach these ideas to students. You can click on the fullscreen "Presentation mode" from the tools on the right-hand side of this page: to make the slide fill the screen. Keep clicking on the ARROW on the RIGHT until it is greyed out/it is no longer possible: to see all the detail on each slide.

## Practice questions

Voronoi - Practice questions to be used alongside the teacher presentation to practice a range of voronoi questions you are likely to be asked in exams.

## IB exam style questions

Voronoi - Exam style exam style questions to test if you feel ready, or what you need to review, ahead of moving on to the new topic or your end of unit test/mocks/final exams!

Voronoi - Exam style questions - follow this link to a page with a further 100 marks worth of questions about Voronoi diagrams

## Teaching Activities

This activity aims to help students develop their own, conceptual understanding of the "toxic waste dump (aka largest circle) problem". It provides a concrete means, via applets, through which students can experiment, using their current knowledge, get feedback, and gradually move towards an appreciation, and understanding, of the Voronoi approach. It links in with slides from the presentation on the "Toxic Waste Problem (aka Large Circle problem)"