Algebra Applications: Floods in Venice

Venice is slowly sinking into the sea

but this is a city that has always embraced the water.

but this is a city that has always embraced the water.

Because the city is at sea level and the water is always

nearby, Venice floods very easily.

For centuries the city has endured constant floods but

now as the city itself begins to sink and the sea level

itself is expected to rise over the next century Venice

finds itself in a struggle for its own survival.

As you can see from above the city is surrounded by water

and its main road is a large canal.

There is a natural barrier that may provide a

possible solution.

One plan under consideration is to build a movable

floodgate that can keep enough water at bay during heavy

storms to keep the city from flooding.

This incredible engineering feet could help keep Venice

dry but this floodgate needs to be activated only when the

sea level reaches a critical level during heavy rains.

But what is the mechanism that would make such a

thing possible?

This complex floodgate would depend on a simple inequality.

If we let x represent the water level, and let A

represent the critical value beyond which the flood gate is

activated then the inequality x is greater than or equal to

A determines when the floodgate is activated.

Let's use the TI-Nspire to create a model of

this inequality.

Turn on the TI-Nspire.

Created a new document.

You may need to save a previous document.

Open a list and spreadsheet window.

Lets define a random variable that will be in the varying

depth of the water around Venice.

We'll let this number vary from 40 to 60 and put this

formula into cell A1 and press ENTER.

This will generate a random number from 40 to 60.

Press CONTROL and R several times to test the function by

generating several random numbers within the set range.

We now need to create a function that tests different

iterations of this random value to see if it has passed

a threshold level.

Press the DOC key and under insert select the

program editor.

At the dialog box create a function called Depth Check

as shown.

Press TAB, the DOWN ARROW twice, and ENTER to

select function.

Press TAB twice to select the OK button and press

ENTER.

Notice that this creates a new tabbed window.

The spreadsheet is still there but in a separate window.

The depth check function will take an input value and

evaluate it.

So input the letter A as shown and press the

DOWN ARROW.

A function always returns a value or an expression.

So we defined the function so that it evaluates input value

A and it returns a message to either raise the

floodgate or not.

For our floodgate suppose that when A is greater than or

equal to 55 the gate needs to go up.

Otherwise the gate stays down.

Input the if statement with the inequality as shown.

Be sure to use the SPACE key between the if and the

variable A and elsewhere as shown.

Once the function is defined press CONTROL and B

to save it.

Use this command any time you make changes to the function.

The function will evaluate the input and will determine if

the floodgate comes up or stays down.

A function like this can be used in a computer program

that controls the floodgate mechanism.

Let's test this function with the spreadsheet value.

Activate the spreadsheet window.

Make sure that cell A2 is the active cell.

Input the newly defined function depth check and have

it evaluate the value in cell A1 where the random var

is generated.

Press ENTER.

Press CONTROL and R several times to test

different values.

You'll notice that for the most part the gate stays down

and comes up only on rare occasions.

This is an accurate model of how the floodgate system would

work, only in the infrequent cases were severe storm is

expected to cause flooding.

Venice is a beautiful city with a glorious history.

Preserving this city may ultimately rely on the inner

workings of an inequality.

[Music]