infinity

INFINITY: It can be smaller than you think

Infinity is big?

Yes or no?

Either way it’s a wonder!

EPISODE 1: Infinity in your hand

Pause the video and work along with the bots.

What the bots do:

The fraction one-half
  • start with 5 identical squares [get the PDF]
  • shade the first square to represent the fraction 1/2
  • shade the second square to represent half of 1/2, or 1/4
  • repeat for fractions 1/8, 1/16 and 1/32
  • use scissors to cut out the shaded parts
  • imagine doing this forever, shading and cutting out
  • then join all the parts to form a new shape
  • how big would the new shape be?

EPISODE 2: Infinity in pieces

Pause the video and work along with the bots.

Some fractions are rectangles; some are squares!

What the bots do:

  • they notice that some of the fractions are rectangles (1/2, 1/8 …), and some are squares (1/4, 1/16…)
  • how much of the square do the rectangular fractions fill?
  • how much of the square do the square fractions fill?

Mathematician Graham Denham (Western University)

See Dr. Denham think through this activity:

EPISODE 3: Infinity art

Pause the video and work along with the bots.

Math art!

What the bots do:

  • the bots notice that the patterns in the square look like art
  • they find new ways of representing the fractions in the square, to create new infinity patterns and new math art

EPISODE 4: Walk out the door

Is it possible to walk out the door?

Try this:

  • walk half way to the door
  • then, walk half of the remaining distance to the door
  • then, walk half of the remaining distance to the door
  • keep doing this forever
  • will you ever get to the door?
  • will you ever walk out the door?
The fractions you walk on the way to the door.

Stuck? Try it another way:

  • forget about the fractions
  • just walk out the door
  • then stop now look back
  • use your imagination to see the infinite number of fractions you walked over

In a song

Preparing to share with family and friends, a group of grade 3 students wrote a skit of what they might say and do if their parents asked them to take out the garbage.

The skit was then turned into lyrics.

See the song performed below by Aboriginal recording artist Tracy Bone and Bob Hallett of Great Big Sea.

EPISODE 5: Does 0.99999… ever end?

Think about this:

  • 0.99999… is the sum of 0.9 + 0.09 + 0.009 + 0.009 + …
  • 0.99999… is the sum of 9/10 + 9/100 + 9/1000 + …
  • the more of its parts that you look at, the closer you get to 1
  • will 0.99999 … ever reach 1?

Try to walk out the door:

  • walk nine tenths of the way to the door
  • then walk nine tenths of the remaining distance to the door
  • then walk nine tenths of the remaining distance to the door
  • keep doing this forever
  • will you ever get to the door?
  • will you ever walk out the door?

Need to think about this some more?

  • 0.99999… = 0.33333… + 0.33333… + 0.33333…
  • 0.33333… = 1/3
  • 1/3 + 1/3 + 1/3 = 1

Mathematician Graham Denham (Western University)

See Dr. Denham think through this activity:

EPISODE 6: Modelling infinity with code

Coming soon.

EPISODE 7: Infinity in history

Coming soon.

EPISODE 8: What have you learned?

Coming soon.