## Welcome to MakerHome

We've completed our yearlong print-a-day project!
All new material is now at Hacktastic: www.mathgrrl.com

## Saturday, June 28, 2014

### Day 306 - Octopus eraser protector

Today, one last print of Cute Octopus Says Hello. We used yesterday's "MyLow cheap 2-shell nFyR yRnS" slicing profile so the model would print as a shell with no base, and resized first to 50% as before, and then to 40% after that, to make tiny cute octopus eraser protectors:

Thingiverse link (to the original octopus design): http://www.thingiverse.com/thing:27053
Thingiverse link (to the pre-sliced .makerbot file): http://www.thingiverse.com/thing:405506

For those of you keeping track of time and money, this print takes 7 minutes and uses .74 grams of filament, including the raft. In filament cost that's just under 6 cents if you're using Small spools, and just under 4 cents if you're using Large spools.

Bonus math question: If you decrease the size of a model to 50% scale, and then decrease the size of that model to 40% scale, how much was the combined percentage decrease? Is is 90% maybe? Or 200%? Try to guess before you read on.

Okay, here's the math: Each scaling changes the linear dimensions of the model. Suppose the model starts out with length L in the x-axis direction. Then changing to 50% scale changes that length to 0.5*L. And changing that model to 40% scale changes the length to 0.4*(0.5*L). Since the product of 0.4 and 0.5 is 0.20, this means that the final model is at 20% scale when compared to the original.

For example, if your original model were 50mm across, then the 50% scale model would be 25mm across, and the 40% scale model of that would be 10mm across (note each 10% of the 25mm model is 2.5mm so 40% is 4*2.5=10mm, so that makes sense). Doing the scaling all at once, a 20% scale model of a 50mm object would be 10mm across (again, each 10% of 50mm is 5mm, so 20% is 2*5=10mm, so that makes sense too).

Want to check your answer without algebra or arithmetic? Do it graphically, by scaling both ways with the octopus model! We get the same tiny eraser-protecting octopus if we scale to 50% and then 40% as we do if we scale all at once to 20%:

Next time: Back to easy again, with a good first print for a classroom setting.