Math Trail
The Vancouver Metropolitan Area, also known as "The Lower Mainland" or the "Greater Vancouver Regional District (GVRD)", is not really one city but many. Due to a steady increase in population in the last 20 years these cities have grown together and are often collectively known as Vancouver even though technically this is not the case.
Before we begin looking at "The Lower Mainland" let's discuss how the province of British Columbia compares to the rest of Canada. Consider the information taken from the 2001 and 1996 Census data:
| Name | Population | |
|---|---|---|
| 2001 | 1996 | |
| Canada | 30,007,094 | 28,846,761 |
| Newfoundland and Labrador | 512,930 | 551,792 |
| Prince Edward Island | 135,294 | 134,557 |
| Nova Scotia | 908,007 | 909,282 |
| New Brunswick | 729,498 | 738,133 |
| Quebec | 7,237,479 | 7,138,795 |
| Ontario | 11,410,046 | 10,753,573 |
| Manitoba | 1,119,583 | 1,113,898 |
| Saskatchewan | 978,933 | 990,237 |
| Alberta | 2,974,807 | 2,696,826 |
| British Columbia | 3,907,738 | 3,724,500 |
| Yukon Territory | 28,674 | 30,766 |
| Northwest Territories | 37,360 | 39,672 |
| Nunavut | 26,745 | 24,730 |
1. What province contains the largest percentage of the population? What is this percentage? Solution
2. How has British Columbia's population changed from 1996 to 2001? Can you state this change as a percentage? Solution
For the purpose of this Math Trail, we will consider the "Lower Mainland" to be a grouping of 18 cities:
|
Map Courtesy of http://www.foundlocally.com/Vancouver/Travel/Maps.htm
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Consider the population of a number of the cities that make up the Lower Mainland:
| Name | Population | |
|---|---|---|
| 2001 | 1996 | |
| Canada | 30,007,094 | 28,846,761 |
| British Columbia | 3,907,738 | 3,724,500 |
| Burnaby | 193,954 | 179,209 |
| Richmond | 164,345 | 148,867 |
| Surrey | 347,825 | 304,477 |
| Vancouver | 545,671 | 514,008 |
3. What percentage of the British Columbia population was found in the city of Richmond in 2001? Solution
One of the main causes of traffic problems in the city is the geography of the area as well as the roadway infrastructure that is being overtaxed. The fact that the two arms of the Fraser River surround much of the Lower Mainland means that anyone travelling must cross a number of bridges each day. (And this is quite different from many other cities who traffic flow is not contained by the "bottleneck" of bridges.)
The website Vancouver: Spectacular By Nature offers the following description of the Lower Mainland as it relates to the city of Vancouver. "The city is on the western-most part of a peninsula that is a major extension of the Fraser River's delta. Several self-governing urban areas called municipalities make up Greater Vancouver. Six of them-Burnaby, New Westminster, Coquitlam, Port Coquitlam and Port Moody-are east of Vancouver. North Vancouver and West Vancouver (located on the "North Shore") are to the north of Vancouver, separated from it by Burrard Inlet."
 |
"The southern boundary of
the City of Vancouver is the North Arm of the Fraser River, one of the
largest rivers entering the Pacific. On the opposite shore of the Fraser
River are the lowland Greater Vancouver municipalities: Richmond, Delta,
Surrey, White Rock and Langley.
Thirty-eight kilometres (24 miles) south of downtown Vancouver is the Canada-US boundary." To see a better view of the Lower Mainland (or GVRD) check out this PDF file. |
| The need for bridges is clearly evident given all the
water that exists in and around the Vancouver area but it is astounding
to think that there are 9 bridges and one tunnel spanning different arms
of the Fraser River and the Burrard Inlet. 4. How many bodies of water (if any) exist around your city or town? How many bridges have been built to cross these expanses? Solution
|
 |
To get us started thinking about what it means to have to cross many bridges consider a Math problem first considered a long time ago:
A Classic Math Problem: The Seven Bridges of Konigsberg
| There was a city in Germany called Konigsberg that was a lot like Vancouver in that it had a river running through and around it. There was even an island in the middle of the river after which the river separated into two parts. Seven bridges were built so that the people of the city could get from one part to another. A crude map of the center of Konigsberg might look like this: |  Courtesy: Math Forum Graph Theory |
The people wondered whether or not one could walk around the city in a way that would involve crossing each bridge exactly once. Actually a famous Mathematician Leonard Euler also took the time to think about this and actually came up with a proof to show that there is no solution. See the Math Forum Explanation.
You may want to work on this problem with your teacher and fellow classmates as it is quite difficult. For more help check out the following website: Math Forum Graph Theory.
So is there other similar problems for which there might be a solution? The answer is yes and let's have a look at that:
| 5. (BONUS QUESTION) Suppose you removed one of the bridges as in the diagram to the right? Can you solve the problem now? Solution |  |
6. Using the rough diagram of the bridges (and tunnel) surrounding Vancouver can you determine how many ways (using different bridge combinations) there are to get from Surrey to Downtown Vancouver? Solution
As we begin to think about more questions concerning traffic let's take a moment to brainstorm about the reason that traffic occurs. For example, bridges that create "bottleneck" situations are one problem.
7. Create a list describing a number of different reasons for traffic jams and congestion in the Lower Mainland? Are these different from the reasons that there may or may not be traffic where you live? Solution
What
do you suppose is the fastest way to get around Vancouver?
At
certain times, for example at two o'clock in the morning, it is definitely
the fastest to travel by car. However,
at other times – rush hour – it is actually just as fast, if not faster
to bike than to drive if the place you are going is less than 5 km away!
Despite
this shocking fact, of the 28% of people live within 5 km of their work, only
16% of them biked to work at least once in 6 months.
(Information taken from the TransLink (BC Public Transit) website and the Statistics Canada website.)
8.
What percentage of the total population does this 16% represent?
In
Vancouver, it is actually possible to bike almost year round, since it almost
never snows. There are many
beautiful streets and paths set apart for cycling around Vancouver, such as
the sea wall.
9.
Why do you think more people do not cycle?
A
big reason for many people is that they feel it is not very safe to cycle.
53%
of drivers, 39 % of recreational cyclists, and 34 % of non-recreational
cyclists believe that cycling is not safe.
In
2001, the number of people injured in traffic accidents (as reported to the
police) was 27, 314. Of this
number, 1007 were bicyclists, 1723 were pedestrians, 23 620 were in a
vehicle, 819 were motorcyclists, and 145 were in some other mode of
transportation.
10.
What percentage of the victims were cyclists? Pedestrians? In
a vehicle? Based on your calculations,
what do you think is the most dangerous form of transportation?
Of
course, if you are in a collision while riding your bike, the potential of
getting hurt is much greater than if you are in a vehicle because you are so
much more vulnerable. However,
out of the 414 people who died in collisions in 2001, only 4 were cyclists.
56 were pedestrians, 319 were in a vehicle, and 32 were on a
motorcycle.
11. What percentage of the fatalities were in each type of transportation? Which do you think is the most dangerous form, and do the statistics agree? What important fact is missing from these statistics? Solution