Golden Ratio & Apple Cores

@BHSGeomety students recently studied the Golden Ratio and Golden Rectangles with a number of different activities.  For example, in one activity students found lengths on different measurements on their face and bodies and calculated to see if any of their ratios were "golden".

The activity I want to share about goes a little something like this...

1.  Give each student (or group of students) an apple.  Have the student cut the apple horizontally so that the cross section is a circle and it exposes the core.

2.  As you can see, the inside of the core has a pentagram shape.  This is one of many instances of the golden ratio found in the natural world.  We had students take a picture of their apple cores and import them into Geometer's Sketchpad.  Our document camera was extremely efficient at doing this.

3.  Using a regular pentagon custom tool in GSP, students constructed the pentagon around their apple core.

4.  Students then compared each other's apple core to see which had the most "golden" core.

This is a fun 10-minute activity that integrates technology and is very hands-on and student centered.  Students were interested to see what each other's cores looked like.  We actually used four different types of apples in our experiment.  No one type of apple seemed to be any more or less golden than the others.

Here are a few more examples: