Stretchy Shapes: Why a Donut and a Coffee Cup Are Twins
Grab a rubber band. Stretch it into a circle. Now squish it into an oval. It's still one rubber band loop — you didn't cut it or glue on a new piece. Topologists (say it: tuh-PAH-luh-jists) are scientists who study shapes like this. They don't care if a shape gets stretched, squished, or bent. They only care about one big rule: did you cut a hole, or seal one up?
What You'll Learn
- What a topologist studies - Why squishing and stretching don't make a new shape - Why a donut and a coffee mug count as the 'same' shape to a topologist - How to count holes in different objects
One Hole Makes You Family
A donut has one hole in the middle. A coffee mug has one hole too — it's the hole your finger goes through in the handle! Roll playdough into a donut shape, then slowly push and pull it without poking any new holes or closing the one you have. You can turn it into a mug shape: the hole in the donut becomes the hole in the handle. To a topologist, a donut and a mug are the same shape, because you never cut or sealed a hole to change one into the other.
Roll playdough into a donut ring. Squish one side flat to make a cup shape, keeping the ring part as a handle. You just topologically transformed a donut into a mug — with zero cuts!
Zero Holes, One Hole, Two Holes
Count holes to sort shapes like a topologist: Zero holes: a ball, an egg, a slice of bread (no hole all the way through) One hole: a donut, a coffee mug, a rubber band loop, a hula hoop Two holes: a pair of scissors (two finger holes), a button with two holes The number of holes is the one thing that does NOT change when you stretch or squish a shape — it only changes if you cut a new hole or seal one shut.
Match each object to its hole count.
Terms
Definitions
Drag terms onto their definitions, or click a term then click a definition to match.
You have a ball of clay shaped like an egg, with zero holes. You squish and stretch it (no cutting) into a long snake shape. How many holes does it have now?
Which pair of objects would a topologist call 'the same shape'?
Hole-Counting Scavenger Hunt
Walk around your home or classroom with a grown-up. Find 5 objects. For each one, count the holes that go all the way through (a hole you could poke a string through). Draw each object and write its hole number next to it. Which object had the most holes?
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