# dy/dan: Domino skyscraper

With Canary Wharf being one of the United Kingdom’s main financial centres, a giant domino adjacent to One Canada Square might be expected to cause some degree of disruption. What would be needed to topple the domino?

Dan Mayer’s ‘Three Act Math’ task ‘Domino skyscraper’ begins with a series of dominos being set up. The dominos form a geometric sequence, with the dimensions of each subsequent domino increasing by a factor of 1.5. Which domino in the sequence would be sufficient to topple a skyscraper sized domino?

Additional information for ‘Act 2’ of the lesson is that the size of a regular domino is 5 cm, the height of Canary Wharf is 235 metres. The calculation becomes one of determining n in

5 × 1.5^{n} = 23 500

So

1.5^{n} = 4 700

It is possible to use more advanced mathematics, but the problem can provide an opportunity for calculator work along with trial and improvement. The answer of a mere 21 dominos also has the advantage of a ‘wow’ factor, demonstrating the rapid growth of geometric progressions.

A possible extension to the task would be to calculate the combined volume of the dominos used and express this as a fraction of the skyscraper sized domino.

We have recently added Dan Mayer’s __‘dy/dan Three Act Math’__ materials to our resources e-library, this example being __‘Domino skyscraper’__.

You can also join us at the National STEM Centre in York to experience ideas for teaching through understanding on the following Enthuse funded courses: __more information can be found here____.__

## howardat58

What is the spacing of the dominos?