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.
Students can use the "student sheet" below this presentation as a summary of the slides over which to add their annotations and notes.
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.
Student Sheet (to accompany above presentation)
This activity requires a helpful review of the pre-requisite knowledge for Voronoi diagrams: 
Parallel and Perpendicular lines
Voronoi Notes from Presentation to Annotate questions to be used alongside the teacher presentation to practice a range of voronoi questions you are likely to be asked in exams (same as the "Practice question" below).
Practice questions
Don't forget the page on Perpendicular Bisectors & Voronoi Diagrams in your eBook where you can learn, review and practise all the key ideas. (Think about opening it in a new tab to keep pages open side by side)
Perpendicular Bisectors & Voronoi Diagrams
In this fascinating topic, we will delve into the wonderful world of Voronoi diagrams. This includes creating Voronoi diagrams with perpendicular bisectors, adding a new site, nearest neighbour interpolation...
Your teacher may set you the following practise tasks
Find the equation of a straight line
There are a number of occasions when you need to know how to find the equation of a straight line function from some given information. In this exercise you will see examples and then practice getting...
Equations of Perpendicular Bisectors
Once you know how to find the equation of a straight line from a point and a gradient, you can solve problems to find the equations of perpendicular bisectors. You need to know how to find the midpoint...
Mid-points and Perpendicular Bisectors
The following questions are designed to build fluency in finding mid-points and the equations of perpendicular bisectors, so that your mind is then free to focus on the context, and using these tools...
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)"
Practise some key skills for coordinate geometry with these activities
Islamic Tile Design
Beautiful, ancient geometry for all of usThis pages offers a short task that you might try as you begin to look at perpendicular bisectors and voronoi diagrams. These incredible designs are undeprinned...
Gradients
Thinking about steepness, parallel and perpendicular linesThe concept of steepness, or Gradient, is a fundamental idea that underpins ideas from linear functions to Calculus! Its important to look at...
Say it both Ways
Recognising, using and switching between these two forms of straight line equationsThis is a short activity aimed at making you familiar with these two forms of a straight line. There are pros and cons...
As the Crow Flies
Which of the lines in the picture is the longest? How can you tell? Are any of them the same length? How do you know? We can all answer these questions with our instincts, we could even get a ruler out...