Slicing and Dicing

To my way of thinking, the topic of Integration is all about 'slicing and dicing' - thinking about what happens when you take an object and chop it into increasingly thinner slices, then put those slices all back together again. Here's a fascinating and gruesome hook I used in my senior mathematics class this year to consolidate* the theme of "slicing and dicing": What would happen if you sliced up a human being?

Warning: This content is only suitable for a senior class, and you should warn students there are medical images coming up. There won't be any blood, but it might affect sensitive students and the dissection of human bodies may not be culturally appropriate in your classroom.

First we start in reverse, using a scene from one of my favourite science fiction films "The Fifth Element"

Then let your students know the images of the human body used aren't computer generated, but actually come from The Visible Human Project. Cue in this video clip:

My students were grossed out and fascinated - and then asked to see it several more times! It took them a while to come to terms with the fact the images weren't generated using a medical scanning device, but by actually slicing up a body. Lots of questions followed!

Depending on time and if you think this is a good idea or not, there are some websites where students can use an online Java application to dynamically explore the data by selecting their own slices in any orientation and see the resulting image created by reassembling the original slices to your specification. 

Here are two websites I found worth exploring:

http://visiblehuman.epfl.ch/index.php

http://visiblehuman.epfl.ch/index.php

Where to next? Many options for discussion about: 

• the mathematics and computation required to reassemble the data so that different views can be constructed.
• the ethics of using bodies from condemned prisoners for science.
• the value of the data from The Visible Human Project - there were scientific as well as ethical criticisms of the project.
• Recent advances in 3D printing technology to "print" biological components using layers of living cells. A long term goal is to print transplant organs using cells from the donor. A quality video from ABC Catalyst program at http://www.abc.net.au/catalyst/stories/3618385.htm (starting at 00:03:00).

One of my students later told me the data from The Visible Human Project is also used in a (rather violent) Japanese manga film Gantz.

(*) I used this lesson idea in the middle of the topic sequence. For my first Integration lesson, I went down a different path - but that's for the next post!  Part 2: Exploring Inequality