## 07 October 2015

### 3-Act Math Images - Circular Farms

I really like this satellite image from NASA of center-pivot irrigated farm in Kansas - it looks like hundreds of pennies to me.

What questions could we ask with this image? Image: Dalhart Texas, NASA Visualization
Some of my ideas:
• How much land goes unused in this image because the fields are planted as circles?
• If you could add smaller center-pivot sprinklers in the corners of the fields (and therefore, smaller circles) to cover some of the unused land, how many sprinklers would you need to cover over 98% of a field?
• What proportion of this land is covered in dark farms, and in light colored farms?
• Assuming irrigation costs were the same for both fields, how much more money could a farm make that planted in rectangular plots instead of circular plots of wheat?
• Which setup would best maximize use of the land - one big center pivot sprinkler (one circle on a square plot, two sprinklers that do a half rotation (two hemispheres on a square plot), or four smaller sprinklers that do full rotations (four circles on a square plot)?