# Transcript: Student Session 22 | Aug 24, 1998

The opening slate pops up with a countdown timer from 5 seconds and the title “TVO’s Virtual Classroom. Get connected.”The “V” in “Virtual” is a tick, the “A” in “classroom” is an at sign with an extended loop that turns into a power cord with a plug at the end, and the first “O” in “classroom” is a spinning globe.

Lorraine and Stewart sit one next to the other in the studio. Lorraine is in her thirties, with short brown hair tied-up and bangs. She’s wearing a black jacket over a white shirt. He’s in his fifties, with a dark beard and wavy brown hair. He’s wearing glasses, a white T-shirt with a colourful geometrical drawing and patterned suspenders.

He says WELCOME TO SESSION NUMBER 22

OF THE VIRTUAL CLASSROOM,

THE MATH MYSTERY.

WE'RE GETTING REALLY

CLOSE TO THE END.

WHAT DO YOU SAY, LORRAINE?

Lorraine says WELL, SESSION 22,

IT'S HARD TO BELIEVE.

WE'RE ALREADY THERE.

He says OH YEAH, AND I THINK TODAY

IT'S GOING TO BE VERY

INTERESTING BECAUSE WHAT WE

ARE GOING TO TRY TO DO IS GET

YOU TO DO THE MATHEMATICS IN

THE LITTLE EXERCISE WITH US,

TOGETHER, AND WE'RE JUST

GOING TO SORT OF STRETCH IT

OUT AND GIVE YOU

ENOUGH TIME TO DO IT.

SO I HOPE YOU -- WE'VE GOT

AN AGENDA HERE, AND I THINK

WE'LL GO TO THAT RIGHT AWAY.

She says OKAY, AND FOR

YOUR AGENDA TODAY:

The slate changes to “Agenda. 1. Sphinx Problem. 2. Pythagorean Theorem. 3. Activity.”

He says NOW, IN TERMS OF THE SPHINX

PROBLEM, THE ONLY THING I WANT

TO CLARIFY, I THINK I

MISINTERPRETED A PHONE CALL

YESTERDAY AFTERNOON WHEN

SOMEBODY SAID IT WAS

IMPOSSIBLE TO DO THREE SPHINX.

AND I'M GOING TO GET A PEN

HERE AND JUST REMIND YOU WHAT

I MEANT BY A THREE SPHINX.

THAT'S WHERE YOU HAD THREE

BASICALLY ALONG THE BOTTOM.

AND I SAID IT WAS POSSIBLE

TO DO IT WITH ONLY FOUR.

I DIDN'T QUITE MEAN THAT.

WHAT I'M SAYING IS THAT THE

THREE SPHINX PROBLEM IS

POSSIBLE, BUT YOU ACTUALLY

NEED 12 SPHINXES TO DO IT.

THAT'S THE CLARIFICATION.

I'M GOING TO LEAVE THAT

PROBLEM FOR YOU TO DEAL WITH

BETWEEN NOW AND THURSDAY.

AND IF WE DO HAVE ANY

RESPONSES BY FAX, THEN IN FACT

WE WILL SHOW YOUR DIAGRAMS,

SEE THE CONSTRUCTION OF A

THREE SPHINX.

OKAY.

SO THAT'S ABOUT IT.

IF THERE'S ANY QUESTION,

DON'T HESITATE TO ASK US.

BUT THAT'S THE CLARIFICATION

I WANTED TO MAKE.

OKAY, WE'RE GOING FROM THE

SPHINX PROBLEM NOW TO THE

PYTHAGOREAN THEOREM.

AND WHAT I WOULD REALLY LIKE

TO DO IS INVITE A STUDENT TO

PHONE IN AND LET US KNOW WHAT

THE PYTHAGOREAN THEOREM IS

AND MAKE A STATEMENT OF IT.

I WILL MAYBE MAKE SOME NOTES,

AND THEN WE WILL, PERHAPS,

HAVE A SLATE OR SOMETHING

LIKE THAT TO MAKE SURE

THE WORDING IS QUITE RIGHT.

SO HAVE WE GOT

ANY PHONE CALLS?

ANYBODY CALLING IN YET?

She says YES, WE HAVE A FEW HERE.

He says GREAT.

She says AND WE'RE GOING TO

CONNECT WITH JACK MINER.

He says OH, GOOD.

She says MEGAN FROM JACK MINER.

He says HELLO, MEGAN,

ARE YOU THERE?

Megan says YEAH.

HELLO?

GIVE IT!

PLEASE!

He says HELLO?

Megan says HELLO.

He says HI, MEGAN.

Megan says HI.

He says CAN YOU TELL ME WHAT THE

PYTHAGOREAN THEOREM IS

ALL ABOUT?

Megan says I DON'T KNOW.

DOES ANYONE HERE KNOW?

He says PARDON?

Megan says NO, I'M JUST ASKING.

NO ONE HERE KNOWS.

SORRY.

Lorraine says THAT'S OKAY.

THANKS, MEGAN.

Megan says OKEY DOKE, BYE.

Lorraine LET'S TRY SOMEONE

FROM THE PINES.

He says OKAY, GREAT.

THE PYTHAGOREAN THEOREM IS

MAYBE THE MOST IMPORTANT

THEOREM YOU EVER LEARN ABOUT.

SO THIS IS ONE I'D

REALLY LIKE TO REINFORCE.

HAVE WE GOT A CONNECTION?

Lorraine says YES, SARAH FROM THE PINES.

HELLO?

Sarah says HI.

IT'S WHEN YOU HAVE A

TRIANGLE, AND YOU'RE GIVEN THE

LENGTH OF TWO SIDES AND YOU

TRY TO FIND OUT THE THIRD ONE

WITH WHAT YOU'VE BEEN GIVEN.

He says THAT'S RIGHT.

SO THE LENGTH OF

TWO SIDES OF A WHAT?

Sarah says TRIANGLE?

He asks ANY SPECIAL KIND OF TRIANGLE?

Sarah says A RIGHT ANGLE.

He says A RIGHT TRIANGLE.

OKAY, SO YOU SAID IN A RIGHT

TRIANGLE, AND I THINK THAT'S A

REALLY IMPORTANT POINT, THAT

IF YOU ARE GIVEN TWO SIDES,

SAY YOU KNOW THIS ONE HERE

AND THIS ONE THERE, YOU CAN

FIGURE OUT THIS ONE HERE.

THAT KIND OF THING?

Stewart draws a right triangle.

Sarah says YEAH.

He says CAN YOU SEE MY DIAGRAM?

Sarah says YEAH.

He says OKAY, WELL, LET'S

GO ONE STEP FURTHER.

HOW?

Stewart appears on a small window at the right bottom of the screen.

Sarah says WE LABEL THEM SO THAT THE

ANGLE ON THE LEFT WOULD BE A.

He says THIS ONE HERE?

Sarah says SURE.

THEN WE CALL THE TWO SIDES

IN THE RIGHT ANGLE B AND X

OR WHATEVER.

He says WHAT I'M GOING TO DO

IS I'LL USE A, B, C.

SO I'LL CALL THIS SIDE

OVER HERE LITTLE C.

SEE WHAT I'M DOING?

THIS ONE OVER HERE LITTLE A,

AND THIS ONE OVER HERE LITTLE B.

OKAY, GREAT.

Sarah says TO FIGURE OUT A, YOU'D PUT B

PLUS C EQUALS THE LENGTH OF A.

He says IT'S NOT JUST STRICTLY B PLUS

C EQUALS THE LENGTH OF A.

YOU'RE CLOSE.

YOU'VE GOT THE RIGHT IDEA.

Sarah says B SQUARED PLUS --

He says AH!

SO...

He writes reads “A square equals B square plus C square.”

He continues WE'LL GO TO A POWER POINT

AND THIS IS THE WAY

IT'S STATED FORMALLY.

IF YOU WANT TO MAKE A NOTE.

IF YOU DIDN'T KNOW THIS

BEFORE, I THINK IT'S IMPORTANT

FOR YOU TO WRITE THIS DOWN.

GO AHEAD.

WHAT'S OUR POWER POINT?

The slate changes to “The Pythagorean Theorem. The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the square on the other two sides.”

He continues NOW, BELIEVE IT OR NOT, THAT'S

EXACTLY WHAT YOU JUST SAID.

AND I WANT TO GO BACK TO THE

GRAPHICS CAMERA AND ILLUSTRATE

THAT ONE A LITTLE

BIT MORE CLEARLY.

WHAT IT SAYS IS IF I WERE

TO DRAW A SQUARE ON THE

HYPOTENUSE -- NOW THE

HYPOTENUSE IS THE LONGEST SIDE

OF A RIGHT-ANGLE TRIANGLE.

IT'S THE SIDE OPPOSITE

THE RIGHT ANGLE.

SO THIS SIDE HERE, WHICH

WILL BE THE LONGEST SIDE.

SO IF I HAD A SQUARE, AND

FOUND THE AREA OF THAT, AND

REMEMBER WHAT WE CALLED THAT

WAS LITTLE A, TIMES LITTLE A,

AND THE AREA OF THIS IS

SQUARED, AND I WERE TO DRAW A

SQUARE ON THE OTHER TWO

SIDES, SOMETHING LIKE THIS.

AND THIS ONE WAS LITTLE B,

SO THAT'S LITTLE B, AND THAT

AREA OF THAT IS B SQUARED.

AND THIS ONE WAS

LITTLE C, SO LITTLE C.

AND THE AREA OF THAT

IS LITTLE C SQUARED.

He draws the figures as he explains them.

He continues THIS BIG SQUARE HAS THE SAME

AREA AS THE COMBINED AREAS OF

THESE TWO.

AND THAT THEOREM HAS

BEEN REALLY, REALLY

IMPORTANT HISTORICALLY.

IT'S A THEOREM, BELIEVE IT

OR NOT, YOU WILL USE OVER

AND OVER AGAIN.

SOMETIMES YOU WON'T EVEN KNOW

YOU ARE USING IT BECAUSE IT

WILL BE IN SOMETHING CALL

THE DISTANCE FORMULA, OR

SOMETHING LIKE THAT, BUT

THE REALITY IS IT'S THE

PYTHAGOREAN THEOREM.

SO I WANTED TO REALLY

MAKE THAT CLEAR.

BECAUSE IN TERMS OF ACTUALLY

DOING THE QUESTIONS FROM

EXERCISE NUMBER ONE, YOU

ACTUALLY HAVE TO USE THE

PYTHAGOREAN THEOREM.

SO I WANT TO LEAVE

THAT RIGHT NOW.

NOW THAT YOU'VE SEEN HOW TO

USE IT, I'M GOING TO ASK YOU

AT LEAST TWICE TO USE IT IN

SOLVING SOME OF THE PROBLEMS

IN EXERCISE NUMBER ONE.

WHAT I WOULD LIKE TO DO RIGHT

NOW IS GO TO QUESTION NUMBER

ONE, AND I'M GOING TO PUT IT

UNDER THE GRAPHICS AND READ IT

TO YOU.

SO WE'LL ZOOM IN A LITTLE BIT.

THAT'S IT.

He shows a piece of paper and reads

THE RATIO OF THE ALTITUDE OF

THE GREAT PYRAMID OF GIZA TO

THE LENGTH OF ONE SIDE OF THE

SQUARE BASE IS APPROXIMATELY

5 TO 8.

He continues NOTICE THAT THOSE NUMBERS

ARE SUBSEQUENT TERMS OF THE

FIBONACCI SEQUENCE?

He reads THE HEIGHT OF THIS PYRAMID

IS RECORDED AS 5,813 INCHES.

He continues WE WORK IN METRIC SO I

CONVERTED IT TO 147.65 METRES.

THE INTERESTING THING ABOUT

5,813, NOTICE THAT 5, 8, AND

13 ARE ALSO FIBONACCI NUMBERS.

IT DOESN'T QUITE WORK SO

NICELY IN THE METRIC SYSTEM.

WHAT I ASKED IS IF YOU KNOW

THE HEIGHT, AND YOU KNOW THE

RATIO, WHAT IS THE LENGTH

OF THE BASE OF THE PYRAMID?

AND I WILL INVITE STUDENTS TO

CALL IN NOW AND MAYBE GIVE US

AN ANSWER.

WE WON'T DO THAT ONE YET.

WHAT I WOULD LIKE TO KNOW

IS IF THE HEIGHT IS 147.65

METRES, AND THE RATIO OF THE

HEIGHT TO THE LENGTH OF ONE

SIDE OF THE SQUARE BASE IS 5

TO 8, WHAT IS, IN FACT, A GOOD

APPROXIMATION FOR THE

LENGTH OF THE BASE.

NO CALLS?

Lorraine says NO, NOT YET.

He continues WELL, I'LL USE THIS.

I MADE IT REALLY BIG, SO

MAYBE WE CAN ZOOM BACK

A LITTLE WEE BIT.

IN OTHER WORDS, WHAT

WE'RE SAYING IS:

He grabs a blue piece of paper that reads “8 to 5 equals base to height. Height is 148 metres. 8 to 5 equals base as compared to 148.”

He continues SO WHAT I WANT TO KNOW RIGHT

NOW IS THIS CHUNK RIGHT HERE.

AS YET NOBODY...

He draws an arrow under “base as compared to 148.”

He continues I'LL GIVE YOU A COUPLE OF

MOMENTS TO MAYBE WORK IT OUT

WITH YOUR CALCULATORS, BUT

WHAT NUMBER WOULD FIT IN HERE?

LOOKS LIKE WE HAVE A CALL.

THAT'S GREAT.

Lorraine says YES, WE HAVE

GABE FROM COLLEGE.

He says GREAT.

Gabe says HELLO?

Lorraine says HELLO.

IS THIS GABE?

Gabe says YEAH.

Lorraine says HI.

He says GREAT.

HAVE YOU DONE A CALCULATION

TO FIGURE OUT THE LENGTH

OF THE BASE?

Gabe says YEAH, I GOT 236.8 METRES.

He says EXCELLENT.

WELL DONE.

THANK YOU, GABE.

AND WHAT I'M GOING TO DO, I

THINK YOU MIGHT HAVE DONE

SOMETHING LIKE THIS.

Stewart grabs another blue piece of paper. It reads “148 divided by 5 times 8 equals B.”

He continues IS THAT MORE OR

LESS WHAT YOU DID?

Gabe says YEAH.

He says FANTASTIC.

YOU SHOULD ALL BE ABLE TO

HANDLE RATIOS LIKE THIS.

I PUT DOWN 237.

IS THAT OKAY WITH YOU, GABE?

Gabe says YEAH.

He says EXCELLENT.

SO WE'VE TAKEN CARE OF THE

FIRST PROBLEM, AND THAT'S HOW

YOU'D DO THE SOLUTION,

AND IT'S ALL DONE.

SO NOW WE CAN GO TO

THE SECOND PROBLEM.

Lorraine says THANKS, GABE.

He says THE SECOND PROBLEM ASKS YOU

TO CONSTRUCT THE GREAT PYRAMID

OF GIZA TO SCALE.

AND THIS IS THE NET.

AND BASICALLY, NOTICE I HAVE

A RIGHT-ANGLE TRIANGLE OVER

HERE ON THE CORNER, WITH THE

ALTITUDE, ONE-HALF THE LENGTH

OF THE BASE.

THE IMPORTANT THING HERE IS

WE NEED TO DISCOVER WHAT THE

SLANT HEIGHT IS SO WE

CAN ACTUALLY MAKE THIS.

NOW, ONE OF THE THINGS I'M

GOING TO COME BACK TO RIGHT

NOW, IF YOU TAKE A LOOK

UNDERNEATH HERE, IS THAT THE

SCALE IS 1 CENTIMETRE

EQUALS TEN METRES.

SO WHAT WE KNOW IS THAT WITH

YOUR PIECE OF CARDBOARD,

THE LENGTH OF THE BASE

IS 23.7 CENTIMETRES.

I'M GOING TO SUGGEST YOU MAKE

IT A NICE EVEN 24 CENTIMETRES

TO MAKE LIFE A LITTLE

WEE BIT EASIER.

NOW, THAT'S BASED ON THE

FACT WE TOOK THIS FIGURE AND

DIVIDED BY TEN, SO WE COULD

GET THE EQUIVALENT IN

CENTIMETRES FOR THE SCALE.

SO I'M SAYING THAT'S KIND

OF EQUAL TO 240 METRES.

SO WHAT WE HAVE RIGHT NOW IS

THAT THIS IS 24 CENTIMETRES,

AND THIS IS 24 CENTIMETRES

GOING UP HERE AS WELL.

OKAY?

SO YOU MAKE A SQUARE.

NOW, WHAT WE NEED TO KNOW IS

THIS LENGTH HERE SO WE GET

TRIANGLES OF THE RIGHT LENGTH.

REMEMBER, THIS IS AS ISOSCELES

TRIANGLE, AND THIS LENGTH HAS

GOT TO BE THE SAME AS THAT.

SO THIS VERTEX IS

RIGHT ABOVE THE MIDDLE.

WHAT WE DO KNOW

IS TWO THINGS.

WE KNOW THAT THE ALTITUDE

IS 148 METRES IN REALITY.

BUT ACCORDING TO OUR SCALE,

DIVIDE BY TEN, IT'S 14.8.

SO WE CAN CALL THAT

15 CENTIMETRES.

AND HALF THE LENGTH OF

BASE IS 12 CENTIMETRES.

AH, HOW AND WHAT DO WE USE TO

FIND OUT THAT LENGTH NOW THAT

WE KNOW THAT THIS IS 15

CENTIMETRES, AND THIS IS

12 CENTIMETRES?

WHAT THEOREM?

Lorraine says WE HAVE VICKI

FROM JACK MINER.

HELLO.

HELLO, VICKI?

He says HI, VICKI?

Kyle says HI.

Lorraine says OH, I DON'T THINK IT'S VICKI.

Kyle says HELLO?

Lorraine says HI, AND YOU ARE...?

Kyle says KYLE.

Stewart says HI, KYLE.

WHAT THEOREM DO WE USE TO

FIGURE OUT WHAT THAT MISSING

SIDE IS?

Kyle says SORRY, I CAN'T HEAR YOU.

WHAT DID YOU SAY?

Stewart says I SAID, WE KNOW THAT IN

THE RIGHT-ANGLE TRIANGLE

THAT THIS IS 15 CENTIMETRES,

AND THAT'S 12.

I WANT TO FIND OUT THE LENGTH

OF THIS OPPOSITE SIDE.

WHAT THEOREM DO I USE?

Kyle says I CAN'T REMEMBER

WHAT YOU HAVE TO DO.

IS IT SIX?

Stewart says OKAY, IT'S THE

PYTHAGOREAN THEOREM.

THAT WAS MY FIRST QUESTION.

WHAT THEOREM.

SO THE PYTHAGOREAN THEOREM.

IS THAT OKAY?

Kyle says I DON'T KNOW WHAT

YOU HAVE TO DO.

Stewart says OKAY.

HAVE WE GOT ANOTHER

CALL, PERHAPS?

Lorraine says YES.

LET'S TRY BRENDA AT THE PINES.

HELLO, BRENDA.

Brenda says HI.

Lorraine says HI.

CAN YOU HELP US OUT THERE?

Brenda says YEAH.

Lorraine says OKAY.

Brenda says YOU HAVE TO USE

PYTHAGOREAN THEOREM.

Lorraine says OKAY, EXCELLENT.

Stewart says RIGHT.

SO HOW WOULD WE USE THE

PYTHAGOREAN THEOREM

TO SOLVE THIS?

Brenda says WELL, THE ONE THAT'S 15

CENTIMETRES, WE COULD SAY

THAT'S A.

Stewart says YEAH.

Brenda says AND 12 IS B.

Stewart says YEAH.

Brenda says C WOULD EQUAL A SQUARED PLUS

B SQUARED, WHICH IS EQUAL TO

12 SQUARED PLUS 15 SQUARED.

Stewart says OKAY.

15 SQUARED IS 225,

I'LL HELP YOU ON THAT.

PLUS 144.

SO WHAT DOES THAT EQUAL?

Brenda says 369.

Stewart says RIGHT.

NOW, WHAT DO I DO WITH THIS?

NOW THAT I HAVE 369, IS THAT

THE LENGTH OF THE OTHER SIDE?

Brenda says YOU HAVE TO DIVIDE IT BY 10.

Stewart says NOT QUITE.

NOW, REMEMBER THE PYTHAGOREAN

THEOREM SAID A SQUARED PLUS

B SQUARED EQUALS C SQUARED.

Brenda says YOU HAVE TO FIND

THE SQUARE ROOT.

Stewart says SO THIS IS EQUAL

TO C SQUARED.

Brenda says YOU HAVE TO FIND

THE SQUARE ROOT.

Stewart says EXCELLENT.

THAT'S WHAT I WAS AFTER.

HAVE YOU GOT A

CALCULATOR HANDY?

CAN YOU FIND ME

A SQUARE ROOT?

Brenda says YEAH, JUST A MINUTE.

Stewart says EXCELLENT.

KIDS ARE WORKING WELL TODAY.

Brenda says 19.2.

Stewart says EXCELLENT.

AND THAT IS A REALLY IMPORTANT

MEASUREMENT IN TERMS OF

ACTUALLY MAKING

THE SCALE MODEL.

SO WHAT WE'RE GOING TO DO AT

THIS POINT, HOPEFULLY I CAN

PUT THIS BIG PIECE OF

CARDBOARD ON HERE BECAUSE WE

STARTED IT, AND THIS IS WHAT

WE ARE GOING TO ASK YOU TO DO

WHEN WE CUT AWAY FOR

ABOUT 12 MINUTES OR SO.

LET'S SEE IF WE CAN

GET ALL THIS ON HERE.

WE'RE GOING TO LOOK AT

THE GRAPHICS CAMERA.

Lorraine says OKAY, AND I'LL OPEN THAT OUT.

A zoom-out view homes out of a drawing. It features a square with four triangles attached to it. One of them is made up of two small triangles.

Stewart says OKAY.

SO THIS IS A NET.

ONE OF THE THINGS YOU'RE GOING

TO NOTICE IS THIS ONE OVER

HERE IS IN THE WRONG PLACE.

ONE OF THE REASONS IT'S IN THE

WRONG PLACE IS THIS CARDBOARD

ISN'T QUITE BIG ENOUGH

FOR ME TO DO IT.

SO WHAT I'M GOING TO DO

ACTUALLY IS I'M GOING TO CUT

THIS TRIANGLE OUT SEPARATELY,

AND I'M GOING TO USE SOME

MASKING TAPE TO TAPE

IT GOING THAT WAY.

He points to the top of the square.

He continues THEN THE REST OF THIS NET I

CAN CUT OUT, AND WE CAN FOLD

IT IN AND THEN TAPE THE EDGES.

BUT LET ME SHOW YOU, FIRST OF

ALL, WE'LL ZOOM IN A LITTLE

BIT UP IN THIS CORNER.

The camera focuses on the triangle made up of two smaller triangles.

He continues JUST SO YOU KNOW HOW TO

CONSTRUCT THE TRIANGLES, FIRST

OF ALL THE SQUARE IS 24

CENTIMETRES SQUARED, AND YOU

HAVE TO MAKE SURE YOU HAVE

NICE SQUARE CORNERS ALL THE

WAY AROUND.

AND IF YOU USE A PROTRACTOR

THAT MIGHT BE GOOD.

THERE ARE SEVERAL METHODS

FOR MAKING SURE THAT

THEY ARE SQUARE.

FIND THE MIDPOINT, WHICH WOULD

BE 12 CENTIMETRES THIS WAY,

AND 12 CENTIMETRES THERE.

AND WHAT YOU WANT TO DO AGAIN

IS TO DRAW A LINE WHICH IS

PERPENDICULAR TO THIS LINE

HERE, SO JUST A LINE LIKE THIS.

THE KEY THING HERE IS THAT

THIS IS 19.2 CENTIMETRES LONG.

SO YOU MEASURE FROM HERE

TO HERE, 19.2 CENTIMETRES.

ONCE YOU'VE GOT THAT, THEN YOU

JUST CONNECT THOSE, AND YOU

HAVE YOUR TRIANGLE.

IF YOU DO THAT ON ALL FOUR

SIDES, IN ESSENCE, AND FOLD IT

IN AND SO ON, YOU WILL

HAVE A SCALE MODEL OF

THE PYRAMID OF GIZA.

DO WE HAVE ANY

QUESTIONS OR ANYTHING?

Lorraine says NO.

He continues NO?

OKAY, SO I THINK AS LONG AS YOU

UNDERSTAND WHAT THE TASK IS,

GET SOME CARDBOARD, AND GROUPS

OF TWO OR THREE, DEPENDING

UPON HOW YOUR TEACHER HAS

ARRANGED IT TO BASICALLY BEGIN

TO PRODUCE A PYRAMID OF GIZA,

USING THE NET, AND ALL THE

CORRECT MEASUREMENTS, FOLD

IT IN AND TAPE THE EDGES.

AND WE'LL COME BACK IN

ABOUT 12 MINUTES OR SO.

ANYTHING TO ADD, LORRAINE?

Lorraine says NO.

IT'S A LOT OF FUN,

ACTUALLY, TO BUILD.

He says AND WHEN WE COME BACK, WE'RE

GOING TO FINISH THIS ONE

OURSELVES, WHAT DO YOU THINK?

Lorraine says THAT'S RIGHT.

SO IF YOU DO HAVE ANY

QUESTIONS IN THE MEANTIME

DURING OUR ACTIVITY, FEEL FREE

TO CALL BY PRESSING POUND NINE.

AND THE ACTIVITY BEING:

The slate changes to “Construct a pyramid model of the Great Pyramid of Gizeh.” A caption appears on screen. It reads “Back in 12 minutes.”

Lorraine says ENJOY.

After a few minutes, Lorraine says HELLO, AMBER?

Amber says HELLO.

Lorraine says HI.

Amber says HI.

Lorraine says DO YOU HAVE A QUESTION?

Amber says NO, SOME IDIOT IN MY

CLASS PUSHED MY NUMBER.

Lorraine says THANKS, AMBER.

HELLO, PING?

HELLO?

HELLO, COLLEGE AVENUE, I BELIEVE

WE HAVE PING CALLING IN?

Ping says HELLO?

Lorraine says HI.

DO YOU HAVE A QUESTION?

Pink says YEAH.

DOES THE SKYDOME HAVE

ANYTHING TO DO WITH THIS?

Lorraine says CAN YOU REPEAT THE QUESTION?

Ping says WHAT ARE THE MEASUREMENTS?

Stewart says WHAT ARE THE MEASUREMENTS?

Ping says YES.

Stewart says THE SQUARE IS 24 CENTIMETRES

BY 24 CENTIMETRES.

THE SQUARE IS 24 BY 24.

THESE TRIANGLES, THE VERTEX

UP HERE IS STRAIGHT OVER THE

CENTRE, SO 12, 12.

BUT THIS LENGTH HERE IS 19.2

CENTIMETRES, AND EACH ONE OF

THE TRIANGLES IS IDENTICAL.

Ping says OKAY, THANKS.

BYE.

Lorraine says BYE.

A woman says HELLO?

Lorraine says HELLO, SARAH?

The woman says SHE LEFT THE ROOM.

I THINK SHE WENT

TO THE WASHROOM.

Lorraine says PARDON ME?

The woman says I THINK SHE WENT

TO THE WASHROOM.

I'M SORRY, SHE JUST LEFT.

Lorraine says OKAY, THANKS.

DO YOU HAVE A QUESTION?

HELLO, GABE?

She appears on a small window at the right bottom of the screen.

Mike says NO, MIKE.

Lorraine says PARDON ME?

Mike says HELLO?

Lorraine says HI, DO YOU HAVE A QUESTION?

Mike says WILL WE BE ABLE TO READ

MORE INFORMATION ON EGYPT?

Stewart says TO GIVE US MORE

INFORMATION ABOUT EGYPT?

Mike says YES, BECAUSE YOU

DIDN'T LET US READ ALL OF

OUR INFORMATION YESTERDAY.

Stewart says WHAT HAPPENED WAS IS THERE

WAS A COMPUTER CRASH YESTERDAY

WHILE YOU WERE ON.

THAT WAS DEFINITELY

NOT PLANNED.

Mike says CAN WE READ THE

REST TODAY THEN?

Stewart says HOW MUCH MORE HAVE YOU GOT,

JUST TO GIVE US AN IDEA?

Mike says JUST EGYPTIAN ART

AND ARCHITECTURE.

Stewart says I DON'T SEE WHY NOT RIGHT

NEAR THE END OF THE PROGRAM.

Lorraine says SURE.

Mike says OH, WAIT.

MY COUSIN WANTS

TO TALK TO YOU.

Nadepa says HE'S COMING!

Mike says SORRY THAT WAS NADEPA.

HE'S KIND OF MESSED

IN THE BRAIN.

BYE.

Lorraine says AND WE HAVE ABOUT

ONE MINUTE TO GO.

WE'LL BE BACK THEN.

After a few minutes, Stewart says HI, WE'RE BACK.

AND RIGHT IN FRONT OF US, WE

HAVE COMPLETED OUR SCALE MODEL

OF THE PYRAMID OF GIZA.

Lorraine says THAT'S RIGHT.

WE'LL MOVE OUR

OTHER ONE AWAY.

Stewart says WHAT DO YOU THINK, LORRAINE?

LOOK PRETTY GOOD TO YOU?

Lorraine says CERTAINLY.

WE CAN EVEN SHOW IT UNDER

OUR GRAPHICS CAMERA.

ISN'T IT BEAUTIFUL?

Stewart says IT'S NOT TOO BAD AT ALL.

Lorraine says VERY PROUD.

Stewart says YEAH, WE FEEL PRETTY GOOD.

AND I HOPE YOU'VE HAD AN

OPPORTUNITY TO ACTUALLY

COMPLETE ONE YOURSELF, OR

SEVERAL IN YOUR CLASSES.

BUT IT'LL GIVE YOU SOME SENSE

OF WHAT THIS LOOKS LIKE

PROPORTIONALLY, AND

THAT'S KIND OF NICE.

WE ASKED ONE OTHER QUESTION

BECAUSE ONE OF THE THINGS THAT

I THINK, QUESTION NUMBER THREE

GETS AT THE WHOLE IDEA OF IF

I WANTED TO FIND THE VOLUME OF

THIS, WHAT FORMULA WOULD I USE?

AND YOU KNOW, OFF THE TOP OF

MY HEAD, I'M NOT 100 PERCENT

SURE WHAT FORMULA

I SHOULD USE.

SO WE'VE DEVISED A LITTLE

BIT OF AN EXPERIMENT.

I'M GOING TO BRING IN JUST AT

THIS POINT, PERHAPS WE CAN

MOVE THAT ONE OVER.

Lorraine says CERTAINLY.

Stewart says WE'RE NOT GOING TO USE THAT

ONE BECAUSE IT'S ACTUALLY

VERY, VERY LARGE.

I'M GOING TO STAND UP NOW, AND

I'M GOING TO BRING IN THIS

LITTLE PIECE RIGHT HERE.

MAYBE WE CAN LOOK AT IT

FROM THE GRAPHICS CAMERA

POINT OF VIEW.

Lorraine says CERTAINLY.

Stewart says THERE IT IS.

IT'S NOT NEARLY AS BIG AS THE

OTHER ONE, AND ACTUALLY IF

YOU REALLY WERE STARING...

Lorraine says IF WE WERE TO COMPARE.

Stewart says YOU CAN SEE THIS ONE

IS QUITE A BIT LARGER.

NOW, THE AMOUNT OF SUGAR I

WOULD NEED FOR THAT WOULD BE A

LOT MORE THAN THE SUGAR I

WOULD NEED FOR THIS ONE.

SO WE'VE DECIDED

TO USE THIS ONE.

NOW, ONE OF THE THINGS THAT

I WANT TO DO IS, FIRST OF ALL,

DETERMINE THE IMPORTANT

DIMENSIONS OF THIS

PARTICULAR PYRAMID.

AND I MIGHT ASK FOR

YOUR HELP A LITTLE BIT.

HERE'S WHAT WE KNOW.

WE'LL GO TO THE

GRAPHICS CAMERA.

HERE'S WHAT WE DO KNOW.

WE KNOW THAT THE SQUARE OF

THE BASE IS 19 CENTIMETRES

BY 19 CENTIMETRES, OKAY?

He draws a square and continues

THE OTHER THING THAT WE

KNOW, AND WE CAN DO THIS BY

MEASUREMENT IS -- THIS

IS NOT A SCALE MODEL.

IT'S NOT INTENDED TO BE.

BUT WHAT WE DO KNOW IS

THAT THE SLANT HEIGHT IS

14 CENTIMETRES.

MEANING HALFWAY ALONG

HERE IS 9.5 CENTIMETRE.

WHOOPS, I SAID

THE SLANT HEIGHT.

14 CENTIMETRES IS

THE SLANT HEIGHT.

WE CAN DO THAT STRICTLY

BY MEASUREMENT.

THIS IS 9.5 CENTIMETRES HERE.

NOW, I WANT TO KNOW HOW LONG

THIS SIDE OF THE TRIANGLE IS.

THIS ONE OVER HERE.

I'LL CALL IT X.

AND I WOULD CERTAINLY BE

INTERESTED IF ANYBODY IS

INTERESTED IN HELPING ME, LET

ME KNOW WHAT WE USE TO FIND

OUT WHAT THE MISSING SIDE IS.

BECAUSE WHAT WE ARE

ACTUALLY FINDING --

OH, I'M GOING TO REDRAW.

IT'S ONE OF THOSE DAYS.

LET'S USE THIS ONE OVER HERE.

THIS IS BETTER.

Lorraine says THIS WAS THE SIZE OF IT.

Stewart says THERE WE ARE.

A boy says HELLO?

Stewart says THERE'S THE PIECE.

I'M GOING TO SLIDE IT KIND OF

OVER A LITTLE BIT HERE SO WE

CAN GET A PROPER LOOK AT IT.

Lorraine says HELLO.

The boy says HI.

Lorraine and Stewart say HI.

Stewart says OKAY, NOW I'M GOING TO

GO BACK TO MY DIAGRAM.

JUST BEAR WITH ME

FOR A MOMENT OR TWO.

The boy says SURE.

Stewart says I HAVE A TRIANGLE.

AND I THINK WHEN I DO IT THIS

WAY I'M GOING TO BE A LOT

SAFER THAN THE OTHER ONE.

IT'S A RIGHT-ANGLE TRIANGLE.

WE KNOW THE SLANT HEIGHT

IS 14 CENTIMETRES.

WE KNOW THIS SECTION ALONG

HERE IS 9.5 CENTIMETRES.

WHAT I WANT TO KNOW

IS THIS HEIGHT HERE?

WHAT THEOREM WOULD I USE?

The boy says WHICH TRIANGLE ARE YOU USING?

BECAUSE FOR SLANT

HEIGHT, I HAVE 19.2.

Stewart says WHAT I WAS SAYING AT THE

BEGINNING IS, YES, YOU'RE

RIGHT, 19.2 CENTIMETRES IS

THE SLANT HEIGHT OF THIS ONE,

WHICH IS THE SCALE MODEL.

BUT FOR DOING THE

EXPERIMENT, WE ACTUALLY

MADE UP A SMALLER ONE.

AND WE HAVE TO GET THE

DIMENSIONS OF THIS SMALLER

ONE BECAUSE I DON'T HAVE

ENOUGH SUGAR TO FILL THIS.

The boy says OH, OKAY.

Stewart says SO I'M GOING TO ASK

THE QUESTION AGAIN.

WHAT THEOREM AM I GOING TO

USE TO FIND THIS HEIGHT HERE,

WHICH IS WHAT I REALLY WANT.

The boy says WELL, YOU'D USE

PYTHAGOREAN THEOREM.

Stewart says EXACTLY.

NOW, CAN YOU HELP ME.

WHAT IS THE CALCULATION THIS

TIME, AND BE REALLY CAREFUL

BECAUSE THIS IS A SLIGHTLY

DIFFERENT ARRANGEMENT THAN

THE OTHER ONE.

The boy says WOULD YOU DO 9.5 SQUARED?

Stewart says PLUS WHAT SQUARED?

The boy says THEN YOU'D FIND THE SQUARE

ROOT, OR WHATEVER THAT IS,

THEN YOU'D SUBTRACT

THAT FROM 14 SQUARED.

Stewart says EXCELLENT, OKAY.

YOU'VE SAID IT CORRECTLY.

WHAT YOU ARE ACTUALLY TELLING

ME IS THAT YOU WOULD ADD THIS

SQUARED AND THAT SQUARED,

THE ONE I DON'T KNOW,

EQUALS 14 SQUARED.

THEN YOU SAID SUBTRACT.

SO IN OTHER WORDS...

On a new piece of paper he writes “X squared equals 14 squared subtracts 9.5 squared.”

Stewart continues NOW, CAN YOU DO A CALCULATION

FOR ME WITH A CALCULATOR?

FIRST OF ALL, BEFORE YOU TAKE

A SQUARE ROOT, FIND OUT WHAT

THAT DIFFERENCE IS.

The boy says I'VE GOT TO GET

A CALCULATOR.

Stewart says THAT'S FINE.

GO RIGHT AHEAD.

VERY GOOD.

The boy says OKAY, HOLD ON.

Stewart says YEAH, NO PROBLEM.

The boy says WE'RE EVEN GETTING A

COMPUTERIZED CALCULATOR.

Stewart says HEY, THEY'RE EVEN

BETTER, AREN'T THEY?

Lorraine says THAT'S RIGHT.

The boy says OKAY, 14 SQUARED...

Lorraine says PARDON?

The boy says WE'RE JUST WORKING IT OUT.

Stewart says IT'S JUST HAPPENING.

THAT'S GOOD.

THAT WAS VERY, VERY GOOD

TO RECOGNIZE IT'S NOT THE

STRAIGHT ADD AND TAKE THE

SQUARE ROOT BUT SUBTRACT

AND TAKE THE SQUARE ROOT

BECAUSE IT'S A DIFFERENT SIDE

IN THE TRIANGLE.

Lorraine says OBVIOUSLY THEY'RE

COMFORTABLE WITH THE THEOREM.

Stewart says THE THEOREM, IF YOU BEGIN TO

UNDERSTAND HOW TO WORK WITH

WHICHEVER SIDE IS MISSING,

THEN YOU'RE IN GREAT SHAPE.

Lorraine says AND SOMETIMES IT'S EASIER IF

THE STUDENTS THINK OF THIS

AS A, FOR THE ONES THAT MIGHT

FIND IT A LITTLE MORE

DIFFICULT, AND THEN

THIS BECOMING B.

Lorraine modifies the equation “9.5 squared plus x squared equals 14 squared.” Where it says “x squared ,” she writes “b squared.”

Stewart says I LIKE MESSING AROUND WITH

LETTERS, YOU KNOW HOW IT IS.

HAVE YOU GOT A NUMBER YET?

The boy says YES, I DO.

IT'S 195.75.

Stewart says I THINK IT'S

105.75, ISN'T IT?

The boy says WE HAVE 195.75.

Stewart says DOUBLE CHECK IT BECAUSE

14 SQUARED IS 196.

AND 9.5 SQUARED.

SO I THINK IT MAY JUST

BE A PUNCHING ERROR.

IS 90.25.

SO IT'S GOT TO

BE CLOSE TO 105.

The boy says OKAY.

Stewart says NOW, WHAT'S THE SQUARE

ROOT OF THIS, 105.75,

APPROXIMATELY?

JUST ONE DECIMAL.

The boy says I DON'T KNOW.

Stewart says OKAY, I'LL HELP YOU OUT.

I'VE GOT A CALCULATOR HERE.

I'LL GET MY CALCULATOR, AND

I'LL TAKE THE SQUARE ROOT

OF 105.75.

AND I GET 10.28,

WHICH IS ABOUT 10.3.

The boy says OH, OKAY.

Stewart says IS THAT GOOD?

The boy says ALL RIGHT, YEAH,

THAT SOUNDS GOOD.

Stewart says SO WHAT WE HAVE NOW IS THE

HEIGHT OF THIS PYRAMID IS

10.3 CENTIMETRES.

NOW, I THINK WHAT WE'VE

GOT TO DO IS DEMONSTRATE

HOW WE DID THIS.

NOTICE THAT WE HAVE

THE TOP OF THIS OPEN.

DON'T OPEN IT UP TOO MUCH.

BUT WHAT WE'RE GOING TO DO

HERE IS WE SET UP THIS FUNNEL

SCENARIO, AND WE HAVE SOME

SUGAR, MAYBE WE CAN PUT A

LITTLE WEE BIT IN.

YEAH.

AND WHAT WE DID IS WE

BASICALLY FILLED THIS THING

RIGHT UP TO THE TOP WITH

SUGAR, AS CLOSE AS WE COULD

GET TO THE TOP WITHIN REASON.

IT WOULD SPILL OUT A BIT.

IF WE MISS A LITTLE BIT AT THE

TOP, IT WON'T BE ENOUGH TO

MAKE A DIFFERENCE.

SO YOU WOULD FILL IT UP.

NOW, WHAT WE'RE GOING TO DO

NOW IS FIND OUT HOW MUCH SUGAR

IS IN THERE AND USE, WHAT

DO YOU CALL THESE THINGS,

LORRAINE?

Lorraine says YES, LOVELY CYLINDER HERE.

Stewart says GRADUATED CYLINDERS.

THERE WE ARE.

Lorraine says THIS IS WHERE IT GETS FUN.

Stewart turns the pyramid upside down and the sugar pours into a cylinder.

Stewart says NOW, I DON'T KNOW HOW MUCH IS

GOING TO BE IN HERE BUT, YOU

KNOW, WE BETTER BE READY WITH

ANOTHER ONE IN CASE THERE IS

MORE SUGAR THAN WE THINK.

IT'S FILLING FAIRLY RAPIDLY.

THAT'S GOOD.

WITH A LITTLE BIT OF LUCK

WE'LL BE FINE ON THIS.

WE'RE ALREADY UP TO 600 MLS.

UH-OH.

GOTTA BE READY,

GOTTA BE READY.

THERE.

As Stewart holds the pyramid, Lorraine changes the cylinder.

He continues NOW, WE'LL HAVE TO TOP IT UP

A LITTLE BIT, BUT I THINK,

YEAH, SO WE'RE

DOING PRETTY WELL.

THAT WAS PRETTY GOOD.

OH, WE REALLY PUT

MORE SUGAR IN THERE.

Lorraine says WELL, WE'VE GOT

QUITE A BIT TO ADD.

Stewart says WE'VE GOT A BIT TO

ADD THERE, THAT'S GOOD.

LET'S SEE.

WE'RE GOING TO TOP

THAT UP TO A THOUSAND.

CAN YOU SHAKE THAT AROUND?

WE'VE GOT A LITTLE

BIT MORE TO ADD THERE.

OKAY, SHAKE IT AROUND.

OKAY, THAT'S GOOD.

SO THERE'S THE AMOUNT OF

SUGAR WE FOUND IN THERE.

IF WE ACTUALLY READ THE TWO

AMOUNTS, THERE'S 1000 IN HERE,

AND THIS IS VERY,

VERY CLOSE TO 380.

SO WE FOUND THE VOLUME OF

THIS IN MILLILITRES ANYWAY.

AND I'M GOING TO MOVE

THAT TO THE SIDE.

WE HAVE 1380 MILLILITRES.

I'M GOING TO CALL IT --

He writes reads “1380.”

Stewart continues NORMALLY, WITH WATER,

1 MILLILITRE EQUALS 1 CC, AND

I THINK FOR THE PURPOSE OF

OUR LITTLE EXPERIMENT, WE'RE

GOING TO ACTUALLY STICK

WITH THAT IDEA.

SO IT'S CUBIC CENTIMETRES,

CENTIMETRES CUBED.

NOW, THE INTERESTING SIDE OF

THIS IS, IF WE TAKE THIS,

I'M GOING TO COME

BACK TO THIS AGAIN.

IF THIS WAS A BOX, A

RECTANGULAR PRISM BOX, AND IT

HAD THE SAME HEIGHT AS THE

HEIGHT, AND THAT'S WHY I

WANTED TO CALCULATE THAT, WE

HAD THE SAME HEIGHT AS THIS,

WITH THE SAME BASE, WHAT

WOULD THE VOLUME BE?

WELL, THE VOLUME WOULD BE

LENGTH TIMES WIDTH TIMES HEIGHT.

SO IF I PUT THAT IN A BOX SO

THE HEIGHT WOULD JUST FIT IN,

THEN I'D GET A BOX:

He writes “Length times width times height equals 19 times 19 times 10.3.”

He continues WHAT WE'RE GOING TO DO IS

COMPARE THE VOLUME OF THIS BOX

TO THE VOLUME OF THE SUGAR

THAT WE FOUND AND SEE IF

THERE'S SOMETHING INTERESTING.

SO I'M GOING TO GET

MY CALCULATOR AGAIN

AND CALCULATE THAT.

SO 19 SQUARED, TIMES 10.3.

AND I GET 3,718 -- I'LL

MAKE IT NICE AND ROUND.

3,720 CENTIMETRES CUBED.

I'M CURIOUS TO KNOW WHAT

FRACTION THIS IS OF THAT.

SO I WILL TAKE 1380 AND I'M

GOING TO DIVIDE BY 3,720.

LET'S SEE WHAT WE GET.

OKAY.

AH, YES.

He writes “point 37.”

He continues NOW, THAT FRACTION, REMEMBER,

THIS IS A VERY, VERY, VERY

ROUGH MEASUREMENT.

IN FACT, I'D BE SURPRISED IF

WE WERE REALLY, REALLY CLOSE.

WHAT I DO KNOW IS THE FRACTION

WE WERE ACTUALLY LOOKING

FOR WAS....3 REPEATED, AND THE ANSWER

TO THAT IS ONE-THIRD.

THIS IS VERY CLOSE.

AND IN FACT, GIVEN THE

ACCURACY WITH WHICH WE WERE

MEASURING AND SO ON, I FIGURE

THAT IS EXCEPTIONALLY CLOSE.

NOW, WHAT I'M GOING TO PROPOSE

TO YOU THEN IS THE VOLUME OF

A PYRAMID IS

CALCULATED THIS WAY:

On a new piece of blue paper he writes “Volume of a pyramid.”

He continues AFTER THIS, WE HAVE TWO AREL

QUESTIONS WE ARE GOING TO

TRY YOU OUT WITH.

AND WE'LL GO FROM THERE.

He continues writing “Area of the base times the height times one third. One third times length times width times height.”

He continues WHEN YOU ARE DEALING WITH A

SQUARE BASE PYRAMID, YOU CAN

USE THAT TO FIND THE VOLUME.

THEREFORE, WE CAN FIND THE

VOLUME ALSO OF THE GREAT

PYRAMID OF GIZA.

VERY QUICKLY, THAT WOULD BE:

He writes “One third 237 times 237 the height 148.”

He continues I'M GOING TO DO A QUICK

CALCULATION ON THAT.

He writes “2,771,004 metres cubed.”

He continues THAT IS HUGE.

NOW, WE'VE GOT TWO

AREL QUESTIONS.

ONE OF THE AREL QUESTIONS --

IS IT ABOUT THE

PYRAMIDS THEMSELVES?

Lorraine says CERTAINLY IS.

The slate changes to “Question 1. What did the Egyptians use to make the corners of Pyramids square? 1. Protractor. 2. Sextant. 3. 3, 4, 5 triangle.” A gray bar graph reads “0 per cent.”

The bar graph changes to blue as numbers go up from “6 per cent” to “30 per cent.”

Stewart says HOW MANY?

30 PERCENT.

COME ON, WE CAN GET

A LOT MORE ANSWERS.

LET'S GET A FEW

MORE PERCENT ANYWAY.

A LOT OF PEOPLE SEEM

TO BE GETTING IT RIGHT.

I'M PLEASED ABOUT THAT.

32 PERCENT.

AH, THERE WE COME.

A LOT OF PEOPLE CAME

IN RIGHT ABOUT THERE.

NOW, LET'S PUT

THE GRAPH UP ON THE...

NOW, AS IT TURNS OUT, SOME

PEOPLE THOUGHT THE SEXTANT,

AND A NUMBER OF PEOPLE ARE

THINKING THE 3, 4, 5 TRIANGLE.

THE PROTRACTOR DIDN'T

EXIST AT THE TIME.

SO YOU CAN

ELIMINATE THAT ONE.

THE SEXTANT EXISTED,

PERHAPS BUT WAS NOT

THE INSTRUMENT.

IN FACT, IT'S A

3, 4, 5 TRIANGLE.

A three-bar graph appears. A green bar reads “8,” a purple bar reads “14” and a blue bar reads “11.”

He continues 3, 4, 5, IT'S CALLED

A PYTHAGOREAN TRIPLE.

He draws a right triangle and continues

IT MEANS THIS LENGTH WAS

THREE, THIS LENGTH IS FOUR,

THAT LENGTH IS FIVE.

AND YOU'LL SEE THAT:

He writes “3 squared plus 4 squared equals 25 equals 5 squared.”

He continues SO WHAT THEY DID IS THEY GOT

A PIECE OF ROPE, WHICH WAS

MARKED IN EQUAL LENGTHS.

THE FACT IS, IT'LL BE A

BIG LONG PIECE OF ROPE.

IT'LL BE THREE SPOTS THERE FOR

THE THREE, THEN ANOTHER FOUR...

THEN YOU WOULD FIND

ANOTHER FIVE ACTUALLY.

IF YOU WERE TO PUT A CORNER

HERE, A CORNER HERE, AND

STRETCH IT AROUND TO THE

CORNER HERE, YOU WOULD GET AN

EXACT RIGHT-ANGLE TRIANGLE.

AND THAT'S HOW THEY

DID IT ACTUALLY.

IT'S A MOST INTERESTING

WAY OF DOING IT.

THAT'S ONE OF OUR QUESTIONS.

WE HAVE, ACTUALLY, A

SECOND QUESTION, AS WELL,

WHICH I THINK IS REALLY

APPROPRIATE AT THIS MOMENT.

HERE WE ARE.

The question changes to “Which of the Pyramids has the greatest volume? 1. Number 1. 2. Number 2. 3. Same.” A gray bar graph reads “0 per cent.”

He continues NOW, I WANT YOU TO

TAKE A REALLY CLOSE LOOK.

WE'RE GOING TO LOOK AT

THIS FROM THE FRONT.

WE HAVE TWO PYRAMIDS.

NOW, THEY ARE

BOTH SQUARE BASED.

Talking to Lorraine, he continues YOU CAN HOLD THAT UP.

SHOW THE BOTTOM.

THEY ARE BOTH SQUARE BASED.

BUT THEY ARE A LITTLE BIT

DIFFERENT BECAUSE THIS ONE THE

VERTEX IS SORT OF STRAIGHT

OVER A CORNER, AND THIS ONE

THE VERTEX IS WAY OVER THERE.

NOW, THE QUESTION IS, GO

BACK TO THE QUESTION, HERE'S

NUMBER ONE, THIS IS NUMBER

TWO, WHICH ONE OF THESE HAS

THE BIGGEST VOLUME?

NOW I WOULD REALLY LIKE TO

INVITE PEOPLE TO PHONE IN.

EXCELLENT, EXCELLENT.

The bar graph changes to blue as numbers go up from “8 per cent” to “43 per cent.”

He continues OKAY, LET'S SHOW THE GRAPH.

AND I WOULD LIKE TO INVITE

ANYBODY THAT ANSWERED NUMBER

THREE TO PHONE IN AND EXPLAIN

WHY YOU CHOSE THE SAME.

A three-bar graph appears. A green bar reads 48,” a purple bar reads “5” and a blue bar reads “19.”

Lorraine says AND THEY MAY WANT TO

LOOK AT IT ONE MORE TIME.

REMEMBER THE BASES ARE --

He says THE BASES.

THAT WOULD BE GOOD.

Lorraine says ALRIGHT.

WELL, WE HAVE QUITE A FEW

NAMES HERE THAT HAVE

ANSWERED THREE.

HERE WE GO.

WE'RE CALLING AARON

FROM THE PINES.

Stewart says OH, GREAT.

Lorraine says HELLO?

Aaron says HI.

Lorraine says AND YOU CHOSE NUMBER

THREE FOR AN ANSWER.

WHY IS THAT?

Aaron says BECAUSE THE BASES

ARE THE SAME.

Stewart says OKAY, THAT'S TRUE.

YOU ARE ABSOLUTELY RIGHT.

BUT ONE OTHER THING HAS TO BE

THE SAME TOO, AND WHAT IS IT?

TAKE A LOOK RIGHT

IN FRONT OF ME.

WHAT'S THE SAME ALSO?

Aaron says THEIR HEIGHT.

Stewart says EXACTLY.

EVEN THOUGH THEY ARE SO

TREMENDOUSLY DIFFERENT IN

SHAPE, YOU CAN SEE THIS ONE IS

WAY STRETCHED OUT COMPARED TO

THAT, IF THE BASES ARE THE

SAME, AND THE HEIGHTS ARE THE

SAME, THEN THEY ARE THE SAME.

EXCELLENT.

THAT IS JUST SUPER.

ABSOLUTELY GREAT.

Lorraine says THANK YOU.

Stewart says NOW I HAVE ONE MORE QUESTION

IN THE EXERCISE TO PROPOSE.

I DON'T KNOW IF ANYBODY HAS

INTERNET ACCESSIBILITY HERE IN

THE CLASS, AND PERHAPS WE

HAVE TO LEAVE THIS ONE

UNTIL THURSDAY.

IT'S NOT A BIG QUESTION.

THE QUESTION IS, WHICH

HAS THE BIGGER VOLUME?

THAT IS, THE SKYDOME OR

THE GREAT PYRAMID OF GIZA?

AND MAYBE WE CAN TAKE A CALL

IF SOMEBODY WOULD LIKE TO LET

US KNOW WHAT THEY THINK.

OR IF THEY'VE ACTUALLY CHECKED

THE INTERNET TO SEE WHAT THE

COMPARISON IS.

OH, WE'VE GOT SOMEBODY

FROM SAINT JOHN.

Lorraine says HELLO?

Jacob says HI.

Stewart says HI.

DO YOU HAVE EITHER KNOWLEDGE

OR AN OPINION ABOUT WHICH IS

BIGGER, THE PYRAMID OF

GIZA OR THE SKYDOME?

Jacob says I'M PRETTY WELL SURE THAT

THE GREAT PYRAMID OF GIZA IS

BIGGER THAN THE SKYDOME

AND HAS MORE VOLUME.

Stewart says ACTUALLY, YOUR FEELING

IS A VERY GOOD ONE.

AND, IN FACT, IT IS CORRECT.

WHAT I WOULD INVITE YOU TO

DO, IF YOU GET A CHANCE --

HAVE YOU GOT ACCESSIBILITY

TO THE INTERNET YOURSELF?

Jacob says I GET ABOUT TEN MINUTES

BEFORE MY DAD KICKS ME OFF.

Lorraine laughs.

Stewart says WELL, TEN MINUTES

WOULD DO IT.

THE SKYDOME HAS A WEBSITE,

AND IT WAS ONE OF THE ONES WE

LISTED REALLY, REALLY EARLY IN

THE FIRST WEEK OF THE PROGRAM.

JUST LOOK THEM UP.

THE VOLUME OF THE SKYDOME

IS LISTED AS ONE OF

THEIR STATISTICS.

AND WHAT YOU'RE COMPARING IT TO,

REMEMBER, WE WORKED IT OUT AS:

He shows the piece of paper that reads “2,771,004 metres cubed.”

Stewart continues SO WOULD YOU BE WILLING

TO CHECK THAT OUT FOR US

FOR THURSDAY?

Jacob says SURE.

Lorraine says GREAT.

Jacob says DO YOU HAVE THE

ADDRESS OF THE WEBSITE?

Stewart says AND YOUR NAME IS AGAIN?

Jacob says JACOB.

Stewart says JACOB.

Jacob says DO YOU HAVE THE

WEBSITE ADDRESS?

Stewart says WE'LL BE LOOKING FOR A

PHONE CALL FROM YOU, JACOB?

Jacob says DO YOU HAVE THE ADDRESS?

Stewart says WE MAY HAVE TO GET

BACK TO YOU AFTERWARD.

WE'VE GOT THE WEBSITE

ADDRESSES UPSTAIRS.

Jacob says OKAY, SO BEFORE

THE SHOW IS DONE?

Stewart says WHEN THE SHOW IS DONE,

ACTUALLY -- YOU'RE AT WHICH

SCHOOL AGAIN?

Lorraine says St. JOHN BREBEUF SO

WE CAN MAYBE SEND IT.

WE'LL BROADCAST IT ON

THE SATELLITE FOR YOU.

ON THE SCREEN.

Stewart says SUPER.

Lorraine says GREAT.

THANKS, JACOB.

FOR YOUR HOMEWORK, IF

YOU CAN WRITE THIS DOWN:

WE HAVE TO SOLVE OUR MATH

MYSTERY ON THURSDAY.

The caption changes to “Homework. Sphinx problem. Math Mistery Journals. Outline of Story.”

Stewart says WE HAVE TO SOLVE THE

MYSTERY, YOU WANNA BET.

Stewart says GREAT.

WE JUST HAD A CALL DURING THE

BREAK, AND I THINK WE COULD

TAKE A LITTLE BIT MORE

INFORMATION ABOUT EGYPT

BEFORE WE CLOSE OFF.

COLLEGE AVENUE, WE'LL

ASK YOU TO PHONE IN.

WE WILL ASK YOU TO BE FAIRLY

BRIEF BECAUSE WE ONLY HAVE ONE

OR TWO MINUTES BEFORE

WE HAVE TO SIGN OFF.

Lorraine says THAT'S RIGHT.

THEREFORE, WE'LL START

WITH GABE FROM COLLEGE.

Gabe says HI.

Stewart says HI.

YOU HAD A LITTLE BIT MORE

INFORMATION ABOUT EGYPT.

Gabe says OKAY, BEFORE I READ THE

INFORMATION, OUR TEACHER

WANTED TO FAX IN A SHEET

WITH EGYPTIAN HIEROGLYPHICS.

Stewart says RIGHT.

Gabe says SO COULD YOU SHOW THAT ON

THURSDAY IF YOU GET IT?

HELLO?

Lorraine says YES, YES.

Gabe says OKAY, THANKS.

I'M READING ABOUT --

OKAY, WAIT.

Lorraine says WE'RE HAVING A LITTLE BIT

OF DIFFICULTY HEARING YOU.

Gabe says I'M READING ABOUT EGYPTIAN

ART AND ARCHITECTURE.

Lorraine says OKAY, GREAT.

TALK A LITTLE BIT LOUDER.

Gabe says EGYPTIAN ART AND ARCHITECTURE.

THE BUILDINGS, PAINTINGS,

SCULPTURES...

Stewart says TALK SLOWLY.

PEOPLE WILL NOT BE ABLE TO

UNDERSTAND YOU, INCLUDING ME.

Gabe continues MEDITERRANEAN EXTENDING

WITH FEW INTERRUPTIONS

FROM ABOUT 3000 BC

THROUGH THE 4th CENTURY AD.

THE NATURE OF THE COUNTRY

FERTILIZED AND UNITED

BY THE NILE AND ITS

SEMI-ISOLATION FROM

THE OUTSIDE CULTURAL

INFLUENCES, PRODUCED AN

ARTISTIC STYLE THAT CHANGED

LITTLE DURING ITS LONG PERIOD.

ART IN ALL ITS FORMS

WAS DEVOTED VISIBLY

TO THE SERVICE OF THE

KINGs, THE PHARAOHs,

WHO WAS CONSIDERED

A GOD ON EARTH

TO STATE AND RELIGION.

FROM EARLY TIMES THE

BELIEF IN LIFE AFTER DEATH

DEDICATED THAT THE DEAD BE

BURIED WITH MATERIAL GOODS

TO ENSURE WELL-BEING

FOR ETERNITY.

Stewart says GREAT.

OKAY THANKS VERY MUCH.

WE'VE GOT TO SIGN OFF, SO

WE'LL SEE YOU ON THURSDAY

FOR THE VERY LAST PROGRAM.

Lorraine says YES.

AND I UNDERSTAND

THURSDAY'S SESSION --

Stewart says OH, HECK, WE'RE NOT

GOING TO BE THERE.

IT'S GOING TO Mr. C.

Lorraine says IT'S OUR LAST.

Stewart says MISTER C AND MISSUS G.

WELL, I GUESS THEY'RE

GOING TO HAVE TO TAKE CARE

OF THE MATH QUESTIONS.

Lorraine says THAT'S RIGHT.

Stewart says MISTER I'LL LET THEM KNOW.

Lorraine says AND ANOTHER THING IS TO

LET THE FACILITATOR FROM

COLLEGE AVENUE, IF YOU

COULD CALL THE HELP LINE,

WE'D APPRECIATE THAT.

THANKS.

AND WE'LL SEE YOU -- ACTUALLY,

WE WON'T SEE YOU THURSDAY,

BUT ALL THE BEST.

Stewart says MISTER C AND MISSUS G.

Lorraine says BYE-BYE.

The slate changes to “Please remember to log off! Pick up handset. Press number sign 7. Press 1 to confirm. Hang up handset. See you next time!”

The PowerPoint presentation finishes and a mouse closes windows.

The caption changes to “Skydome website: www.skydome.com.”