Transcript: Student Session 16 | Aug 24, 1998

(music plays)
A white slate appears with the title “TVO’s Virtual Classroom. Get Connected,” and a five seconds countdown at the bottom.

A woman in her late thirties is sitting at a computer. She has red hair tied back, and is wearing a white blouse under a brown blazer.

Lorraine says GOOD AFTERNOON,
AND WELCOME
TO TVO'S VIRTUAL
CLASSROOM.
I'M LORRAINE GOWER,
AND TODAY IS LESSON 16
OF THE MATH MYSTERY.
DURING OUR LESSON TODAY,
WE'RE GOING TO BE
TALKING ABOUT

A blue slate appears with the title “Agenda.” Under the title a numbered list gradually appears “1. Fibonacci. 2. Examples. 3. Activity. 4. Homework.”

Lorraine continues FIBONACCI, WELL,
WHERE DOES IT
COME FROM?
IT'S ACTUALLY A
NAME OF A PERSON.
AND A LITTLE BIT OF
HISTORY ON THAT.

A blue slate appears, with sentences gradually appearing: “Fibonacci’s real name was Leonardo of Pisa. He wrote many books about mathematics. His most famous work in 1202, ‘Liber Abaci’, introduces Arabic numerals into Western Culture.”

Lorraine continues FIBONACCI’S REAL NAME WAS
LEONARDO OF PISA.
THE REASON FOR THAT IS
HE LIVED IN PISA, ITALY,
AND HIS NAME AS LEONARDO,
SO THEY CALLED HIM
LEONARDO OF PISA.
AND HE WAS BORN IN
THE 13TH CENTURY.
SO IN THE 1200s.
AND WE'RE IN THE
WESTERN CULTURE.
NOW, WHEN WE TALK
ABOUT ARABIC NUMERALS,
AND ROMAN NUMERALS, LET'S
SEE WHAT THAT MEANS EXACTLY.

A blue slate appears under the title “Fibonacci.” It shows the numbers from 0 to 9 under the title “Arabic Numerals,” and under “Roman Numerals” the roman numbers from 0 to 9. Then, an example appears: the number “48” in Arabic numerals and “XLVIII” in Roman numerals.

Lorraine continues NOW, IN THE WESTERN
WORLD, WE TENDED TO USE
THE ROMAN NUMERALS
IN THE 1200s,
AND IT WAS FIBONACCI
WHO WAS INTRODUCED
TO THE ARABIC NUMERALS
AND CHANGED IT.
SO SINCE THEN, WE'VE BEEN
USING ARABIC NUMERALS.
NOW, HE NOTED THE NUMBER
48 IN ARABIC NUMERALS
WAS MUCH EASIER TO WRITE
THAN YOU CAN SEE HERE,
48 IN ROMAN
NUMERALS.
HE FOUND THIS SO BE
MUCH MORE EFFICIENT.
NOW, THIS FIBONACCI
FELLOW, AROUND HIM,
HE LOVED TO
SOLVE PROBLEMS,
AND WAS VERY OBSERVANT,
AND HAD A MATHEMATICAL MIND,
AND HE'S THE ONE
THAT CAME UP WITH
THE CONCEPT OF THE
RABBITS THAT YOU'RE GOING
TO HAVE TO FIGURE
OUT FOR THURSDAY.
WELL, I'M GOING TO
HELP YOU UNDERSTAND
THE SEQUENCE THAT
OCCURS IN ORDER FOR YOU
TO UNDERSTAND THIS WHOLE
LESSON ON FIBONACCI.
EVEN ONCE YOU
KNOW THE SEQUENCE,
YOU'RE STILL GOING TO
HAVE TO FIGURE IT OUT
THROUGH THE RABBITS IN
ORDER TO EXPLAIN IT
TO US ON THURSDAY.
BUT THIS WHOLE SEQUENCE,
LET'S HAVE A LOOK AT IT,
AND IF YOU HAVE NOTED THE
PARTICULAR SEQUENCE
AND YOU SEEM TO
UNDERSTAND IT,
OR AT LEAST HAVE SOMEWHAT
OF A CONCEPT OF WHAT
THE FIRST NINE
NUMBERS MIGHT BE,
YOU CAN CALL ME BY
PRESSING #9,
AND WE'LL SHARE IT
IN FURTHER DETAIL.
SO LET'S LOOK AT THE
SCREEN OVER HERE.

A blue slate under the title “Fibonacci Sequence (Infinite sequence) appears. It reads “The first twelve Fibonacci numbers are:”

Lorraine continues FROM THE RABBIT EXERCISE,
SOME OF YOU MAY
HAVE NOTED THERE IS AN
ACTUAL SEQUENCE THERE.
SOME OF YOU MAY NOT HAVE
ATTEMPTED IT YET
BECAUSE IT IS DUE FOR
THURSDAY, BUT WE'RE GOING
TO TALK ABOUT IT SO
YOU UNDERSTAND IT,
AND FROM THERE, YOU'RE
GOING TO SEE IT'S
ALL AROUND US, AND
IT'S VERY EXCITING.
I HAVE SOMEONE FROM
COLLEGE AVENUE.
HELLO?

A man says HELLO?

Lorraine says HI.
DID YOU COME UP
WITH A SEQUENCE?

The man asks FOR WHAT?

Lorraine says FOR THE FIBONACCI
NUMBERS.

The man says YEAH.

Lorraine says OKAY, WHAT DO
YOU HAVE SO FAR?
I'M GOING TO SHOW
IT ON THE SCREEN.
WHAT DO YOU HAVE?
HOW DOES YOUR
SEQUENCE BEGIN?

The man says ONE.

Lorraine says OKAY, VERY GOOD.
ONE.
WHAT ELSE?

The man says TWO, THREE,
FIVE, EIGHT, THIRTEEN TWENTY ONE.

Lorraine writes the numbers in the slate with the computer cursor.

Lorraine asks OKAY, AND WHAT ARE YOU
DOING RIGHT NOW
TO GET THAT SEQUENCE?

The man says I'M ADDING THE NUMBERS
THAT COME BEFORE THAT.

Lorraine says OKAY, CAN YOU GIVE
ME AN EXAMPLE HERE?
THERE ACTUALLY SHOULD BE
ANOTHER ONE OVER HERE.

She writes a one before the first one.

Lorraine continues SO WHAT ARE YOU DOING
HERE TO GET TO
THE NEXT NUMBER
EACH TIME?

The man says ONE PLUS ONE
EQUALS TWO.

Lorraine says THAT'S RIGHT.
AND THEN?

The man says TWO PLUS ONE
EQUALS THREE.

Lorraine says THAT'S RIGHT.
SO WHAT YOU'RE
DOING IS TAKING
THESE TWO NUMBERS AND IT
BECOMES THIS NEXT ONE.
THEN YOU'RE
TAKING THESE TWO,
AND IT'S BRINGING IT
ON TO THE NEXT ONE.
OKAY, EXCELLENT.
THANKS VERY MUCH.

The man says OKAY, COOL.

Lorraine says AND I'M GOING TO
CLEAR THAT OFF HERE,
AND WE'RE GOING TO NOTE,
VERY IMPORTANT YOU
REALIZE THIS IS
ONLY THE FIRST 12.

The first twelve numbers of the sequence appear on the slate: “1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.”

Lorraine continues IT GOES ON TO INFINITY,
SO FOREVER AND EVER
AND EVER, IF YOU WERE
TO CONTINUE ADDING.
SO IF YOU DON'T HAVE
THIS PARTICULAR SEQUENCE
WRITTEN DOWN, I SUGGEST
YOU PROBABLY DO SO
RIGHT NOW BECAUSE WE'RE
GOING TO BE USING IT DURING
THE WHOLE PERIOD SO THERE
IS A GOOD UNDERSTANDING.
AND IN ORDER TO GET EVEN
THE FIRST ONE THERE
IT'S ADDING ZERO TO ONE.
ALL RIGHT, SO NOW THAT
YOU HAVE THAT SEQUENCE
IN FRONT OF YOU, WE'RE
GOING TO BE REFERRING
TO IT SEVERAL TIMES.
AND THE EXAMPLES I'M GOING
TO GIVE YOU RIGHT NOW,
JUST TO LET YOU KNOW
FIBONACCI NUMBERS,
WE SEE THEM IN SPACE,
WE SEE THEM IN NATURE
AS FAR AS PLANTS
AND ANIMALS.
WE SEE THEM IN ART
AND ARCHITECTURE.
WE SEE THEM IN MUSIC.
AS WELL, SCIENCE
AND TECHNOLOGY.
IT'S ALL AROUND US.
AND IN ORDER TO
UNDERSTAND THAT,
I'M GOING TO GIVE
YOU A FEW EXAMPLES.
IT TAKES A WHILE TO
GRASP THE CONCEPT,
AND THEN FROM THERE YOU
ARE GOING TO HAVE
AN ACTIVITY TO SEE IF YOU
CAN COME UP WITH YOUR OWN.
THE FIRST, EASIEST
PROBABLY APPROACH
IS SEEING IT IN NATURE
WITH PLANTS AND SO ON.
AND AN EXAMPLE HERE, I'LL
BRING IT UP A TAD CLOSER.

A drawing of a tree trunk in a sheet of paper appears on screen. It has seven branches alternating at different heights.

Lorraine says IT'S NOT ALL
THAT CLEAR,
BUT I'M SURE
YOU'LL UNDERSTAND.
THIS IS A TREE TRUNK, OR
AN ACTUAL PLANT THAT'S
GROWING WITH BRANCHES
OFF TO THE SIDE HERE.
AND I'VE PUT AN ACTUAL
ARROW TO GO AROUND.
I'LL EXPLAIN THAT.
NOW, I DON'T KNOW
IF YOU'RE FAMILIAR,
BUT PLANTS TEND TO
GROW IN A SPIRAL,
AND THE REASON FOR THAT
IS THEY WANT MOISTURE
AND SUNLIGHT AND AIR, SO
THEY TEND TO ROTATE
TOWARDS THE SUN TO GET
THEIR FOOD AND SO ON.
AND THIS CONCEPT HERE OF
THIS PARTICULAR PLANT,
IS GROWING WITHIN
THREE YEARS.
SO HERE IS THE FIRST
YEAR, THE SECOND YEAR,
AND THE THIRD YEAR.
NOW, IN ONE YEAR, IT
ACTUALLY BRANCHES OUT TWICE.
NOW IN TWO YEARS, YOU'RE
GOING TO NOTICE IT
BRANCHES OUT FIVE TIMES,
AND IN THREE YEARS
IT ACTUALLY BRANCHES OUT
EIGHT BECAUSE THE FOUR
OVER HERE IS ON THE
OTHER SIDE OF THE PLANT,
WE CAN'T SEE IT.
AND HERE IS FIVE,
SIX, SEVEN, EIGHT.
AND WHEN WE THINK
ABOUT THAT,
IT'S ALL FIBONACCI
NUMBERS.

She takes a marker and writes the sequence in the paper.

Lorraine continues BECAUSE YOU'VE
GOT, IN ONE YEAR,
YOU HAVE THE TWO
BRANCHES, OR ACTUALLY,
EVEN TO THE THREE.
AND THEN IN FIVE
YEARS, IN TWO YEARS
YOU HAVE FIVE BRANCHES,
AND THEN IN THREE YEARS,
YOU HAVE THE
EIGHT BRANCHES.
AND IT GOES ON
FROM THERE.
SO IT'S AN APPROACH TOWARDS
THE FIBONACCI NUMBERS.
ALWAYS REFER TO YOUR
SEQUENCE YOU SEE
IN FRONT OF YOU.

She takes a pineapple and holds it on her hand.

She continues AS WELL, I HAVE
HERE A PINEAPPLE.
AND IT SMELLS WONDERFUL.
AND PINEAPPLES ARE VERY
INTERESTING WHEN IT
COMES TO FIBONACCI
NUMBERS, AS WELL.
AND I'LL PUT IT UNDER THE
GRAPHICS CAMERA HERE
SO YOU CAN SEE IT A
LITTLE BIT CLOSER.

She lays the pineapple on the table.

She continues AND THEY'VE DONE MANY
STUDIES AS FAR AS
THE FIBONACCI NUMBERS
FOUND IN THE SEQUENCE
THAT YOU SEE HERE
OF A PINEAPPLE.
AND THEY'VE ACTUALLY
STUDIED MORE THAN 2,000
DIFFERENT PINEAPPLES.
AND WHAT THEY REVEALED
IS THEY ALL HAVE
A FIBONACCI PATTERN.
AND THIS PARTICULAR ONE
I'VE ACTUALLY MARKED HERE.

She turns the pineapple to show eight dots in a diagonal line.

She continues AND YOU'LL NOTE THAT IT
HAS EIGHT PARALLEL ROWS.
AND THE NUMBER EIGHT
BEING IN THE
FIBONACCI SEQUENCE.
AND HERE YOU CAN
SEE WHERE IT STARTS.
THERE'S ONE ROW, TWO,
THREE, FOUR, FIVE, SIX,
SEVEN AND EIGHT.
SO THIS WHOLE CONCEPT OVER
HERE IS ANOTHER EXAMPLE
IN NATURE WHERE YOU CAN
SEE THE FIBONACCI NUMBER.

Lorraine shows a paper with three drawings of pineapples with highlighted diagonal lines in a different angle for each.

She says AND EVEN IN MORE DETAIL,
IF YOU WERE TO LOOK
AT PINEAPPLES, THEY SAY
SOME OF THEM EVEN HAVE
THREE DIFFERENT SPIRAL
PATTERNS, AGAIN,
WITH THE FIBONACCI
NUMBERS.
THIS ONE BEING EIGHT
PARALLEL IN THIS SPACE,
HERE 13, AND HERE 21.
IT'S ALL THE
SAME PINEAPPLE,
WITH THE DIFFERENT
SPIRALING SEQUENCE.
AS WELL, IT'S SEEN IN MANY
OTHER DIFFERENT PLANTS,
WHICH WE'LL SHOW YOU A
FEW MORE LATER WITH
THE VIDEO AND SO ON.
BUT FIBONACCI NUMBERS ARE
ALSO SEEN IN ANIMALS.
AND ONE VERY COMMON
APPROACH HERE
FOR THE ANIMALS
IS THE SPIRAL.
AND I'LL EXPLAIN THAT BY
LOOKING AT THIS PARTICULAR
CONCEPT THAT WE'VE
LOOKED AT BEFORE.

She shows a drawing in a book of a spiral made of squares following the Fibonacci sequence.

Lorraine continues WE'VE TALKED ABOUT THIS
WHOLE THING WHERE
WE HAVE A LITTLE UNIT,
ONE LITTLE SQUARE UNIT,
AND IT'S ATTACHED TO
ANOTHER LITTLE SQUARE UNIT.
YOU SEE A LITTLE
BIT ABOVE IT.
AND THEN IT'S ATTACHED
TO TWO SQUARE UNITS,
THEN TO THREE,
THEN TO FIVE,
AND THESE ARE ALL
FIBONACCI NUMBERS.
1, 2, 3, 5
8, 13, 21, 34,
AND WE KEEP GOING, AS IT
GETS LARGER AND LARGER.
CAN ANYONE CALL ME RIGHT
NOW AND SHARE WITH ME
WHEN DID WE LAST SEE THIS
WITH THE MATH MYSTERY?
AND WHAT DID WE NOTICE
WHEN WE ADDED AN ARC
TO EVERY ONE OF
THOSE SQUARES?
WHAT HAPPENED?
AND WE'RE CALLING
RIGHT NOW THE PINES.
YOU'RE GOING TO
TELL US - HELLO?

A woman says HELLO?

Lorraine says HI, IS THIS PAM?

Pam says YEAH.

Lorraine says HI.
DO YOU REMEMBER
SEEING THIS BEFORE?
WE TALKED ABOUT THIS
PARTICULAR CONCEPT.

Pam says YUP.

Lorraine asks WHAT WAS IT?

Pam says GOLDEN RECTANGLE.

Lorraine says EXACTLY, THE GOLDEN
RECTANGLES ALL OVER THE PLACE.
AND THEY ARE USING ALL
THE TIME THE NUMBERS
IN THE SEQUENCE
OF THE FIBONACCI.
NOW, IF I WAS TO ADD AN
ARC TO ALL OF THESE,
WHAT HAPPENS?

Pam says IT MAKES A SPIRAL.

Lorraine says THAT'S RIGHT.
AND IF WE LOOK AT IT OVER
HERE WE SEE THE IDEA,
AND I'LL BRING IT OUT A
TAD, OF EXACTLY THAT.

She shows the same drawing but with a spiral in it.

Lorraine continues WHERE WE'VE SPIRALED, AND
THE WAY WE WERE LOOKING AT IT
EARLIER
WAS LIKE THIS.
AND WHEN YOU ADD
IT ALL AROUND,
WE SEE THE SPIRALING.
SO THAT'S, AGAIN, A
FIBONACCI APPROACH.
DO YOU KNOW ANY ANIMALS,
PAM, OR ANYTHING OUT THERE
IN THE NATURE THAT HAS THAT
SPIRALING APPROACH TO IT?

Pam says NO.

Lorraine asks CAN YOU THINK
OF SOMETHING?

Pam says WAIT, A SNAIL.

Lorraine shows a drawing depicting the spiral pattern of a snail.

Lorraine says OKAY, VERY GOOD
BECAUSE THAT'S MY NEXT -
HERE, YOU CAN SEE IT'S
KIND OF LIKE THE SNAIL
ABOVE, AND WHAT'S
INTERESTING ABOUT IT
IS IT'S ALL AT 90 DEGREES.
AND WE'RE GOING TO TALK
A LITTLE BIT MORE
ABOUT THAT AFTERWARDS.
GREAT.
THANKS VERY MUCH.

Pam says YOU'RE WELCOME.

Lorraine says AND LOOKING AT THAT AGAIN
IS THAT SPIRALING IDEA.
AND IT'S A CONCEPT OF
THE GOLDEN RECTANGLES,
ALL THE DIFFERENT NUMBERS
OF THAT SEQUENCE.
SO KEEP THAT IN MIND.
IT'S QUITE INTERESTING.
AS WELL, WHEN WE TALK
ABOUT THE GOLDEN
RECTANGLES, WHICH
PAM MENTIONED TO US...
WHAT'S INTERESTING IS WE
MENTIONED ONE BUILDING
IN THE MATH MYSTERY,
AND IT WAS IN GREECE,
ONE PARTICULAR
ARCHITECTURAL BUILDING
THAT WAS BASED A LOT ON
THE GOLDEN RECTANGLE.
CAN ANYONE CALL ME RIGHT
NOW AND SHARE WITH ME
WHAT WAS THAT PARTICULAR
ARCHITECTURAL BUILDING
THAT WE SPOKE ABOUT?
AND I CAN SEE SOMEONE IS
CALLING FROM JACK MINER.
AND ACTUALLY, WE SEE
THIS GOLDEN RECTANGLE
ALL OVER THE PLACE IN
ARCHITECTURE AND IN ART.
AND IT WAS VERY, VERY
SIGNIFICANT AND GREW FROM
THE POINT FIBONACCI
USED HIS SEQUENCE.
AND WE'RE GOING TO TALK
A LITTLE BIT MORE
ABOUT THAT AS WE CONNECT
WITH JACK MINER.
AND BEFORE I SHOW YOU
THE ACTUAL BUILDING...
WE'LL LOOK AT THIS AGAIN,
WHERE WE'RE ACTUALLY
SEEING A BUNCH OF
GOLDEN RECTANGLE,
ALL WITHIN A MUCH LARGER
GOLDEN RECTANGLE.
OKAY?
HELLO?

A woman says HELLO.

Lorraine says HI.
DO YOU REMEMBER THE
BUILDING WE TALKED
ABOUT IN GREECE?

The woman says THE PARTHENON.

Lorraine says EXCELLENT.
THANKS VERY MUCH.
AND STAY ON THE
LINE, PLEASE.

She shows a drawing of the façade of the Parthenon. A note on the top reads “Golden rectangle and golden proportions in the Parthenon.

Lorraine continues AND IF WE LOOK AT THIS,
WHICH EXPLAINS THE PARTHENON,
DO YOU REMEMBER WHERE THE
GOLDEN RECTANGLES WERE?

The woman says REPEAT THE QUESTION.

Lorraine says OH, SURE.
DO YOU REMEMBER WHERE THE
GOLDEN RECTANGLES WERE
ON THE PARTHENON?
DO YOU REMEMBER
HOW MANY?

The woman says NO.

Lorraine says OKAY, CAN YOU TELL ME
WHERE IS THE LARGEST RECTANGLE
THAT YOU SEE FOR THE BUILDING
OF THE PARTHENON?

The woman says THE STEPS WERE
GOLDEN RECTANGLES?

Lorraine says THE STEPS DOWN
BELOW HERE?
THEY'RE JUST A
TAD TOO SMALL.
THEY HAVE TO BE -
THE GOLDEN RECTANGLE,
THE LARGEST ONE IS THIS
ONE RIGHT HERE, OKAY?
AND IF WE GO BACK TO
THIS, THESE ARE
ALL GOLDEN RECTANGLES.
DO YOU SEE THEM?

She shows the squares with the Fibonacci spiral.

Lorraine continues AND THIS ONE WOULD BE
EVEN THAT MUCH LARGER,
AND SO ON.
CAN YOU FIND MORE
IN THE PARTHENON?

The woman says THE TOP?
THE TWO TRIANGLES?

Lorraine says OKAY, EXCELLENT,
THAT'S RIGHT.
WE CAN USE THE
TRIANGLE HERE,
IF WE WERE TO EXTEND
IT, IT WOULD MAKE
A RECTANGLE, WHICH IS
THE GOLDEN TRIANGLE.
OR EVEN THESE SMALL ONES.
DO YOU SEE THE
SMALL ONES HERE?
YES, OR EVEN THE LARGER
ONE RIGHT ACROSS HERE
AND SO ON.
THANKS.
WHAT'S INTERESTING, AND
THE REASON WHY THEY
EVEN BOTHERED CALLING
IT GOLDEN RECTANGLE
IS THEY'VE OBSERVED
THAT THE HUMAN EYE,
WHEN WE TEND TO LOOK
AT A BUNCH OF DIFFERENT
RECTANGLES, FOR INSTANCE,
I'LL SHOW YOU A FEW HERE,
AND WE'LL ZOOM RIGHT IN

She shows several rectangles of different sizes in the book. Two of them are bolded.

Lorraine continues THEY'VE DONE A STUDY
TALKING TO SEVERAL
DIFFERENT HUMAN BEINGS,
AND ASKING THEM TO JUST
LOOK AT A BUNCH
OF RECTANGLES HERE.
THESE WEREN'T DARKENED
OR ANYTHING, AND SAID,
WHICH ONE IS MORE
PLEASING TO THE EYE?
AND IT SEEMS LIKE
THE MAJORITY,
A GREAT MAJORITY,
TENDS TO VISUALIZE
AND APPRECIATE THE
GOLDEN RECTANGLE
AMONGST ALL THE OTHERS.
IT JUST SEEMS TO BE MORE
COMFORTING FOR
THE HUMAN EYE, AND WE
SEE THEM IN MANY AREAS,
SUCH AS PLAYING CARDS.
YOU KNOW WHEN YOU
PLAY WITH THE CARDS,
THAT'S A GOLDEN
RECTANGLE.
A LOT OF THE BOARD GAMES
WE USE, AND SO ON, AND SO ON.
ANOTHER GOLDEN APPROACH
IS THE GOLDEN RATIO.
AND AGAIN, WHY THEY
ARE CALLING IT GOLDEN,
IS IT JUST SEEMS TO BE
THAT MUCH MORE POPULAR,
AND AGAIN, IT'S USING
THE FIBONACCI NUMBERS,
OR THE APPROACH OF THE
SEQUENCE FROM THE FIBONACCI.
AND AN EXAMPLE OF THAT,
OF THE GOLDEN RATIO,
AND TAKE THAT OUT A BIT.

She writes “Golden ratio” in a sheet of paper. Under that she writes “S/L = L/S+L.”

Lorraine continues IF YOU WANT TO
WRITE THIS DOWN,
IT'S KIND OF
INTERESTING.
THE RATIO THAT THEY
ARE TALKING ABOUT IS,
IF YOU HAVE
SOMETHING SMALL,
TO SOMETHING LARGE, IT'S
RELATED TO THAT SAME
LARGE THING TO THE SMALL
AND LARGE TOGETHER.
WELL, WHAT IT IS EXACTLY
I'M TALKING ABOUT.

She shows a drawing of a hand and its bones. They’re named from tip to palm: A, B, C, D.

Lorraine continues FOR INSTANCE, IF WE
THINK OF OUR HAND, OKAY?
THIS SMALLER PORTION OF
THE BONE, RIGHT HERE, A,
SO HERE A IS TO B, AS B,
THIS SECTION IS
TO A PLUS B.

She writes “A/B = B/A+B.”

Lorraine continues ANOTHER WAY OF SAYING IT,
THE SMALLER PART
OF THE BONE IS TO THE
NEXT LARGER ONE,
LIKE B IS A BIT LARGER,
AS THE LARGER ONE
IS TO THE WHOLE
ENTIRE THING.
WHICH WOULD BE THE
WHOLE, OR WE CAN SAY,
THE SMALL PLUS THE LARGE,
WHICH IS THE WHOLE.

She writes “S/L = L/W.”

Lorraine continues AND YOU'RE GOING TO
NOTICE, THIS RATIO HERE,
THIS PART OF THE BONE
IS RELATED TO THIS,
AS THIS IS TO THE
WHOLE SECTION OF THAT.
AND THAT'S THE WHOLE
SEQUENCE OF THE FIBONACCI.
AND WE TEND TO SEE
THAT EVERYWHERE.
JUST LIKE THE
GOLDEN RATIO.
THE ONE SIDE OF THE GOLDEN
RATIO IS TO THE LONGER SIDE,
AS THE LONGER SIDE IS TO
THE WHOLE OF THE TWO.
AND IT GROWS FROM THERE.
AS WELL AS WE'RE
GOING TO NOTICE IT,
AND WE'RE NOT GOING TO
TALK AT THAT JUST YET,
MAYBE YOU CAN DISCOVER
IT IN YOUR ACTIVITY,
BUT WE SEE IT MUSIC,
WE SCIENCE TECHNOLOGY,
WE SEE IT IN SPACE,
IN MANY AREAS.
AND THESE ARE JUST A
FEW OF THE EXAMPLES
WITH THE SPIRALS AND
SO ON, AND THE HANDS,
AND THE DIFFERENT
PROPORTIONS EVEN
ON OUR BODIES AND SO
ON, THAT RELATE
TO THE FIBONACCI NUMBERS.
WHAT I'M WANTING YOU TO DO
IN THE NEXT FIVE MINUTES
IS AN ACTUAL ACTIVITY
WHERE YOU'RE GOING
TO GET TOGETHER
WITH A FRIEND,
OR THE PERSON RIGHT NEXT
TO YOU, AND TALK ABOUT,
SEE HOW MANY, IN
YOUR CLASSROOM,
OR EVEN OUTSIDE THE
CLASSROOM, AREAS,
OR OBJECTS THAT YOU SEE,
THAT ARE RELATED
TO THE FIBONACCI
NUMBERS.
SO YOU DEFINITELY
NEED TO HAVE THEM
IN FRONT OF YOU.
HAVE A LOOK.
HAVE A LOOK AT YOUR
BOOKS, PAPER, THE DESKS,
WHATEVER YOU
SEE AROUND YOU,
AS WELL AS BEYOND THAT,
IF YOU CAN THINK
OF SPACE AND IS ON.
AND THEN WE'RE GOING
TO SHARE OUR IDEAS
ALL TOGETHER, AND SEE HOW IT
RELATES MATHEMATICALLY.
AND JUST TO LET YOU KNOW,
THIS OCCURS YEARLY,
INTERNATIONALLY, WHERE
MATHEMATICIANS ACTUALLY
GET TOGETHER AND TALK
ABOUT FIBONACCI NUMBERS.
SO WE'RE GOING TO PRETEND
WE'RE THE MATHEMATICIANS
AND SEE IF WE COME UP
WITH SIMILAR IDEAS.
IF YOU HAVE ANY QUESTIONS
WITHIN THE FIVE MINUTES,
FEEL FREE TO CALL BY
PRESSING #9.
AND THIS IS
YOUR ACTIVITY.

A blue slate under the title “Activity” appears. It reads “Identify things related to Fibonacci numbers. Ex: 1, 1, 2, 3, 5, 8, 13, 18,… back in 5 minutes.”

Lorraine says WE’LL BE BACK IN FIVE MINUTES
ENJOY.

Lorraine says HI.

A man says HI.
18 ISN'T A
FIBONACCI NUMBER.

Lorraine says WHAT IS IT?

The man says 21.

Lorraine says THAT'S RIGHT.
THANKS VERY MUCH, AND
I'LL PUT MY LITTLE -
I ENJOY USING MY
POWER POINT HERE.
THANKS VERY MUCH.

She scratches out the number 18 in the slate and writes 21 and 34.

Lorraine says AND WHERE AM I HERE.
SO THAT GOES.
HELLO?
HELLO, MEGAN?
FROM JACK MINER.

Megan says HELLO?

Lorraine says HI, DO YOU
HAVE A QUESTION?

Megan says NO.

Lorraine says YOU DON'T?
OKAY, YOUR PHONE
MUST HAVE RUNG.
THANKS.

Lorraine says HELLO.
HI DO YOU HAVE A QUESTION?

A man says HELLO

Lorraine says HI IS THIS DAVID
OR JACOB?

John says NO, THIS IS SHAUN.

Lorraine says SHAUN, DO YOU
HAVE A QUESTION?
BECAUSE YOUR PHONE IS
RINGING FROM HERE.

Shaun says NO, I DON’T HAVE A QUESTION

Lorraine says YOU DON’T, OK
DO YOU UNDERSTAND THE ACTIVITY?

Shaun says PARDON?

Lorraine repeats DO YOU
UNDERSTAND THE ACTIVITY?

Shaun says YES

Lorraine says GREAT, OK.
THANKS.
BYE.

Lorraine says OKAY, NOW IS OUR CHANCE
TO HEAR FROM YOU
THE DIFFERENT
FIBONACCI SEQUENCES,
OR NUMBERS YOU MAY
SEE AROUND YOU
IN YOUR CLASSROOM, OR
OUTSIDE THE CLASSROOM,
AND THEN I WILL SHARE
WITH YOU VERY QUICKLY
IN MUSIC, AND SCIENCE AND
TECHNOLOGY, AND SO ON,
WHICH WILL BE VERY
SIMILAR TO THE ONES
YOU SEE IN YOUR EXERCISES
TO HELP YOU FOR THURSDAY.
SO CALL ME NOW BY
PRESSING #9,
AND SHARE WITH ME WHAT
IT IS YOUR GROUP
PUT TOGETHER AS FAR
AS FIBONACCI NUMBERS.
IT'S VERY IMPORTANT IN
THE MATHEMATICAL WORLD.
IT SEEMS TO BE
ALL AROUND US.
AND WE HAVE SOMEONE
FROM ST. JOHN BREBEUF.
HELLO?

Shaun says HELLO.

Lorraine says HI, WHAT DID
YOU COME UP WITH?

Shaun says FOR WHAT ONE?

Lorraine says FOR ANY.
DID YOU COME UP WITH
ONE THAT'S SPIRAL,
OR THE GOLDEN RECTANGLE,
OR THE GOLDEN RATIO,
AS FAR AS
FIBONACCI NUMBERS.
WHAT DO YOU HAVE?

Shaun says THAT WAS A COUPLE
OF WEEKS AGO.

Lorraine says NO, FOR YOUR
ACTIVITY.
WHAT DID YOU DO IN
THE LAST FEW MINUTES?
IS IT DAVID OR JACOB?

Shaun says IT'S SHAUN.

Lorraine says OH, IT'S SHAUN.
AND SHAUN, WHAT DID YOU DO
IN THE LAST FEW MINUTES
THERE FOR THE ACTIVITY?
DID YOU COME UP
WITH SOME
FIBONACCI NUMBERS
AROUND YOU?

Shaun says NO.

Lorraine says OH, OKAY, WE SEE YOU
DIDN'T DO YOUR WORK.
THANK YOU.
ALL RIGHT, WE'LL GO
TO THE PINES AND SEE
IF THEY'VE PUT
TOGETHER SOME IDEAS.
I BELIEVE IT'S PAM.
LET'S TRY THAT AGAIN.
SO WE'RE CALLING
PAM FROM THE PINES.
HI.

Pam says HI.

Lorraine says DID YOU COME UP WITH SOME
IDEAS FOR THE FIBONACCI?

Pam says YEAH.

Lorraine says OKAY, WHAT DO
YOU HAVE?

Pam says ART.

Lorraine says OKAY, WHAT HAVE
YOU GOT?

Lorraine writes “Art” in a sheet of paper.

Pam says A STAIRCASE
THAT'S A SPIRAL.

Lorraine writes “Staircase (spiral).”

Lorraine says EXCELLENT.
STAIRCASE.
WHICH IS THE SPIRAL.
OKAY, AND
ANYTHING ELSE?

Pam says ANY GOLDEN RECTANGLES.

Lorraine writes “G. Rectangles”

Lorraine says EXACTLY.
WHAT DO YOU HAVE AS FAR
AS THE GOLDEN RECTANGLES?
DO YOU HAVE
SOME EXAMPLES?

Pam says YEAH.
THE CEILING.

Lorraine adds every item Pam says.

Lorraine says OKAY, GOOD.
WHAT ELSE?

Pam says DOORS.

Lorraine says SOME DOORS.
NOT ALL.
BUT DEFINITELY.

Pam says LIGHT SWITCH?

Lorraine says OH, INTERESTING.
YES.
AND ANY OTHERS?

Pam says PAPER.

Lorraine says DEFINITELY SOME
PAPER SIZES.
AND WHAT ELSE MIGHT
YOU HAVE THERE?

Pam says CUPBOARDS.

Lorraine says CUPBOARDS, GOOD.
THANKS VERY MUCH.
GREAT.
OKAY, WE'RE CALLING
SOMEONE FROM USBORNE.
KRISTEN OR CARRIE.
USBORNE CENTRAL.
THESE ARE
EXCELLENT IDEAS.
AS YOU CAN SEE, SO
FAR FROM THE ART,
THE GOLDEN RECTANGLES
WILL STILL
BE ARCHITECTURE, AS
WE'RE NOTICING.
HELLO?

A woman says HELLO.

Lorraine says HI.
WHAT DID YOU
COME UP WITH?

The woman says AN EXAMPLE OF FIBONACCI
IS A SHUFFLEBOARD.

Lorraine says OH, GREAT.
THE SHUFFLEBOARD.
WHAT ELSE?
THAT COULD BE A
GAME, WHICH IS GOOD.
DID YOU COME UP
WITH ANY OTHERS?

Lorraine writes “Shuffleboard (game).”

The woman says A SNAKE SKIN.

Lorraine writes in a new sheet of paper every item the woman says.

Lorraine says WHAT ABOUT
THE SNAKE SKIN?

The woman says THE SCALES.

Lorraine says OH, INTERESTING.
VERY GOOD.
AND WHAT ELSE?

The woman says A PYRAMID.

Lorraine says OH, GOOD.
ANYTHING ELSE?

The woman says THE BOWLING
PIN FORMATION.

Lorraine says AND HOW DO YOU
SEE THAT?

The woman says I DON'T KNOW.

Lorraine says YOU'RE NOT SURE.
THAT'S GOOD.
WELL, THANKS
VERY MUCH.
WE'LL TRY
SOMEONE ELSE.
GOOD.
ARCHITECTURE, ART, AND
WHAT ELSE DO WE HAVE?
HELLO?

A man says HELLO.

Lorraine asks HI, IS THIS ADAM?

Adam says YES.

Lorraine asks WHAT DO YOU HAVE?

Adam says FOR FIBONACCI, A SOCCER
BALL BECAUSE IT HAS
34 DIFFERENT
LITTLE PANELS.

Lorraine adds “soccer ball (34)” to the list.

Lorraine says GREAT.
SOCCER BALL.
ANYTHING ELSE?

Adam says BRANCHES FROM
THE TREES.

Lorraine says OKAY.
ANYTHING ELSE?

Adam says SOME FRUIT.

Lorraine asks AS IN?

Adam says PINEAPPLE.

Lorraine says OKAY, WE'VE SEEN THAT.

Adam says YEAH.

Lorraine asks HAVE YOU COME
UP WITH YOUR OWN?

Adam says SPIRAL.
A TORNADO.

Lorraine says GREAT.
THAT'S WITH
NATURE AND SPACE.
TORNADO.

Adam says MOUNTAINS.

Lorraine says OKAY, MOUNTAINS.

Adam says ICICLES.

Lorraine says OH, VERY GOOD.
ICICLES.
THIS IS NATURE AGAIN.
ANYTHING ELSE?

Adam says DOOR HANDLE.

Lorraine asks AND HOW DO YOU SEE
THE DOOR HANDLE?

Adam says IT TURNS.
THAT'S A SPIRAL.

Lorraine says OKAY, SO SOME FORM A
SPIRAL TO GET IN TO TURN.
EXCELLENT.
THANKS VERY MUCH.
VERY GOOD IDEAS.
SO AS WE CAN SEE, WE'RE
NOTICING IT ALL AROUND US.
AND IT MAKES US A
LITTLE MORE AWARE AND
APPRECIATIVE OF
WHAT THE HUMAN EYE,
OR HOW NATURE
EVEN TENDS,
AND WE'RE NOT
TOO SURE WHY,
BUT TENDS TO FORM
AROUND THE SEQUENCE
THAT FIBONACCI
MANAGED TO DISCOVER.
AND EVEN HERE, WHEN
WE THINK OF MUSIC,
MANY OF THE SYMPHONIES
AND SO ON ARE BASED
WITH FIBONACCI
NUMBERS.
AND IF WE THINK
AS FAR AS PIANO,
ANY INSTRUMENT…

She shows a drawing of piano keys. 5 black in two groups of 2 and 3, and 8 white labeled from left to right “C, D, E, F, G, A, B, C.”

Lorraine says WE WILL
NOTE THAT WE HAVE
HERE AN OCTAVE OF
EIGHT NOTES.
AND HERE AGAIN, EIGHT
BEING FIBONACCI,
AS WELL AS THE
FIVE BLACK NOTES.
AND FROM THE
OCTAVE, AND SO ON,
WHEN WE TALK ABOUT MUSIC,
THERE'S THE CHORDS
IN MUSIC THAT YOU
HEAR ALL THE TIME.
AND IN A CHORD YOU ALWAYS
HAVE THE ROOT, THE THIRD,
AND THE FIFTH, AND
OBVIOUSLY THE OCTAVE.
AND THAT WOULD BE A
MAJOR CHORD, LET'S SAY,
OR EVEN A MINOR CHORD,
AND IT'S ALL BASED,
AGAIN, ON THE
FIBONACCI NUMBERS.
AND FROM THERE,
AS WELL IN NATURE,
OTHER CLIPS I HAVE
HERE IS ON VIDEO,
AND YOU WILL
SEE IN A MOMENT.
NOW, CAN YOU GUESS
WHAT THAT IS?

A clip shows a sunflower.

Lorraine says YES, VERY GOOD, IF
YOU DID DECIDE
IT WAS A SUNFLOWER.
AND WHAT'S INTERESTING
ABOUT THE SUNFLOWER
IS THEY'VE NOTICED THE
USUAL NUMBER OF SPIRALS
IN A SUNFLOWER HEAD
IS 34 GOING ONE WAY,
AND IN THIS CASE,
THERE WE GO,
GOING COUNTER CLOCKWISE.

She draws with the computer cursor a spiral following the pattern in a sunflower picture.

Lorraine continues ALL THESE SPIRALS,
THEY PARALLEL
APPROXIMATELY 34,
AND SPIRALING
THE OTHER WAY,
WHICH WOULD BE CLOCKWISE,
APPROXIMATELY WOULD BE 55.
AND AGAIN THE TWO NUMBERS
BEING THE FIBONACCI.
THE LARGER ONES WOULD
OBVIOUSLY BE 55 AND 89,
AGAIN FIBONACCI, AND YOU
CAN EVEN GET LARGER ONES
THERE, 144 TO
233 PARALLELS.
AND AGAIN, IT'S SPIRALING,
AND USING THE NUMBERS
FROM THE FIBONACCI
SEQUENCE.
THEREFORE, WE'RE
NOTICING IT'S AROUND US,
AND IT'S VERY EXCITING,
AND AS YOU MENTIONED,
A LOT OF THE
GAMES WE PLAY,
EVEN THE BOARD GAMES AND
THE CARDS, AND SO ON,
ARE ALL BASED FROM THE
FIBONACCI NUMBERS.
AND AS A MAIN CONCLUSION,
WHAT'S EXCITING HERE
IS THAT FIBONACCI,
HIMSELF, AS WE MENTIONED,
WAS BORN IN
ITALY, IN PISA,
AND HIS BOOK THAT HE
WROTE IS IN THE LIBRARY
IN FLORENCE, ITALY, WHICH
IS WHERE JEWELS IS HAVING
OUR FRIENDS HERE, RENE,
ISAAC AND SOPHIA,
TRY TO DETERMINE, JUST
LIKE YOU'LL BE DOING
THIS WEEK WITH YOUR
EXERCISES.
AND HIS PARTICULAR
BOOK IS IN THE LIBRARY
IN FLORENCE, ITALY.
AND AS WELL,
FIBONACCI, HIMSELF,
BEING BORN IN PISA, IF
YOU EVER GO THERE AND SEE
THE LEANING TOWER OF PISA,
WHICH WE HAVE OVER HERE...

She shows a drawing of the Leaning Tower of Pisa.

Lorraine continues YOU WILL NOTE, IF YOU
EVER HAVE A CHANCE TO GO,
WHICH IS A VERY EXCITING
AREA, IT'S BEAUTIFUL,
THE LEANING TOWER OF PISA
SHOULD BE LEANING A TAD
MORE LIKE THIS,
AS YOU WILL NOTE,
AND FIBONACCI STATUE IS
ACTUALLY NEXT TO THIS
LEANING TOWER OF PISA.
AND AS I MENTIONED
EARLIER, YEARLY,
APPROXIMATELY 50
MATHEMATICIANS FROM
13 COUNTRIES GATHER TO
EXCHANGE INFORMATION
AND IDEAS ON
MATHEMATICAL TOPICS,
AND THEY ARE ALL RELATING
TO FIBONACCI NUMBERS.
AND THIS HAS BEEN
OCCURRING SINCE 1960.
AND AS WELL, THERE'S A
FIBONACCI ASSOCIATION
IN CALIFORNIA, IN THE
STATES, AND AS WELL,
THEY PUBLISH FIBONACCI
QUARTERLY JOURNALS SINCE 1962.
SO IT IS QUITE POPULAR,
AND LITTLE DID HE KNOW
FROM HIS SEQUENCE HE
REALLY STARTED SOMETHING
AROUND US AND MADE US
MUCH MORE AWARE
OF OUR NATURE AND
SPACE AND MUSIC.
WE TEND TO REALLY DEAL
TOWARDS THESE NUMBERS.
AS YOU KNOW, WE
HAVE FOR THURSDAY,
EXERCISES 1 AND 2,
AND I WILL PUT UP THAT
SLATE IN A FEW MINUTES,
BUT IF YOU HAVE ANY
QUESTIONS ABOUT YOUR
HOMEWORK THAT YOU HAVE
FOR THURSDAY, I'D BE MORE
AND PLEASED TO HELP YOU.
AND ONE EXERCISE HERE
THAT'S SIMILAR TO ONE
OF YOURS, AND THAT WOULD
BE IN SCIENCE AND
TECHNOLOGY IS
AS FOLLOWS.

She shows an exercise in a book with drawings of two glass panes in different positions.

Lorraine says YOU SEE HERE AN
ACTUAL GLASS PANE,
AND THE LIGHT FROM THE
SUN IS ACTUALLY GOING TO
GO THROUGH THE GLASS PANE
HERE, AS YOU CAN TELL.
AND THERE'S MANY
DIFFERENT WAYS THE SUN
WOULD ACTUALLY
SHINE THROUGH THAT.
WHICH IS VERY SIMILAR
TO THE EXERCISE
YOU HAVE ABOUT
YOUR BEES.
IF WE WERE TO SAY, IF A
RAY IS REFLECTED ONCE,
THERE ARE TWO PATHS
IT CAN FOLLOW,
AS YOUR BEES ARE DOING
FROM THE ACTUAL BEEHIVE.

She shows a different page showing how the sun rays reflect when against two glass panes next to each other.

Lorraine continues AND IN THIS CASE, IF
WE HAVE TWO PANES,
THERE ARE TWO WAYS IT
CAN ACTUALLY TRAVEL.
THE SUN CAN GO, HIT THE
FIRST PANE AND COME OUT.
OR IT CAN GO RIGHT
THROUGH AND COME OUT.
NOW, IF WE THINK AGAIN
OF FIBONACCI NUMBERS,
IT CAN GO THAT
MUCH FURTHER.
IF WE'RE THINKING
IT'S REFLECTED TWICE,
THERE ARE THREE PATHS
IT CAN ACTUALLY TAKE.
AND AGAIN, WE'RE
FOLLOWING THAT SEQUENCE.
SO THREE GOING TO THE
FIRST PANE, GOING BACK,
AND REFLECTING THIS WAY,
OR GOING RIGHT ACROSS
THE TWO PANES, COMING
BACK AND GOING ACROSS,
OR A THIRD
APPROXIMATE WAY.
AND THEN AGAIN, IF
IT'S REFLECTED TWICE,
OR THREE TIMES, AS
IN THE SEQUENCE,
HOW MANY TIMES THEN?

She shows a new page with the sun rays reflecting five times and then eight times in the glass panes.

Lorraine continues IT WOULD GO FIVE.
AND THESE ARE THE FIVE
POSSIBLE DIFFERENT WAYS
IT CAN POSSIBLY TAKE.
AND IF WE THINK OF
THE SEQUENCE AGAIN,
IF IT'S REFLECTED FOUR
TIMES, IT WILL THEN,
INSTEAD OF HAVING FIVE,
IT WILL HAVE EIGHT
APPROACHES, WHICH
WE SEE HERE.
AND ALWAYS GOING IN
THE SAME DIRECTION.
SO IT REFLECTS HERE,
BACK, AND THERE'S
EIGHT DIFFERENT
POSSIBILITIES.
SO THE SEQUENCE,
ONCE AGAIN,
IF IT'S ONE REFLECTION,
IT CAN TAKE TWO PATHS.
FROM THE TWO PATHS, IT CAN
TAKE THREE, FROM THREE,
THEN FIVE, THEN
FIVE, THEN EIGHT,
AND IT GOES ON FROM
THERE, JUST LIKE WHAT
YOUR BEES WERE DOING.
SO WITHOUT ANY DELAY
HERE, IF YOU HAVE
ANY QUESTIONS, I'M
NOTICING YOU DON'T,
BUT IN THE NEXT
FIVE MINUTES,
IF YOU HAVE ANY QUESTIONS
CONCERNING YOUR EXERCISES 1
OR 2, I'D BE MORE THAN
PLEASED TO HELP YOU OUT.
ENJOY.

A blue slate under the title “Homework” appears. It reads “Exercises 1 and 2 for Thursday.”

Lorraine says HELLO, STACIE?

Stacie says HI.

Lorraine asks DO YOU HAVE A QUESTION?

Stacie says YEAH.
ARE THE MOON
PHASES RELATED
TO THE FIBONACCI
NUMBERS?

Lorraine asks ARE THEY WHAT?

Stacie asks ARE THEY RELATED
TO THE NUMBERS?
THE MOON PHASES?

Lorraine says OH, EXCELLENT
QUESTION.
I'M NOT TOO SURE.
I CAN CHECK INTO THAT,
AND I'LL LET YOU KNOW
ON THURSDAY.
AND MAYBE YOU
COULD AS WELL,
AND WE'LL
LOOK AT THAT.
OKAY, GREAT,
THANKS.

Stacie says BYE.

Lorraine says BYE.

Lorraine says GOOD AFTERNOON, AND WELCOME
TO THE VIRTUAL CLASSROOM.
I'M LORRAINE GOWER.
AND I'M GOING TO SHOW
YOU WHAT I HAVE
ACCESS TO IN
FRONT OF ME.
I HAVE A QUESTRON.
AND I'M GOING TO TEACH A
QUICK MINI MATH LESSON
ON FIBONACCI, AND THIS WAY
YOU'LL HAVE A CHANCE
TO SEE WHAT IT IS I'M
ABLE TO SHOW YOU,
AS IF YOU WERE THE
STUDENT, OKAY?
AND THEREFORE, IF I
WANTED TO EXPLAIN
TO YOU FIBONACCI, AND
WHERE IT CAME FROM,
I COULD THEN GO
TO MY PC HERE

A blue slate appears, with sentences gradually appearing: “Fibonacci’s real name was Leonardo of Pisa. He wrote many books about mathematics. His most famous work in 1202, ‘Liber Abaci’, introduces Arabic numerals into Western Culture.”

Lorraine continues AND EXPLAIN TO YOU THAT
FIBONACCI'S REAL NAME,
WHO HAPPENED TO BE A MAN,
IS LEONARDO OF PISA,
AND HE'S FROM THE
AREA OF PISA IN ITALY.
AND THAT'S WHY THEY CALLED
HIM LEONARDO OF PISA.
AND HE CHOSE THE
NAME FIBONACCI.
AND HE WROTE MANY BOOKS
ABOUT MATHEMATICS.
THIS BOOK IS NOW IN
FLORENCE, ITALY,
IN THE LIBRARY THERE.
AND IF I WANTED
TO GO FURTHER ON…

A blue slate appears under the title “Fibonacci.” It shows the numbers from 0 to 9 under the title “Arabic Numerals,” and under “Roman Numerals” the roman numbers from 0 to 9. Then, an example appears: the number “48” in Arabic numerals and “XLVIII” in Roman numerals.

Lorraine continues I WOULD THEN BE ABLE TO
SHOW THE STUDENTS THE
ARABIC NUMERALS INSTEAD
OF THE ROMAN NUMERALS,
AND HOW MUCH
SIMPLER IT IS,
AND THAT'S WHY
HE CHOSE THAT.
AS WELL, FIBONACCI IS WELL
KNOWN FOR A PARTICULAR
SEQUENCE HE DISCOVERED.
AND I WILL SHOW YOU THIS.
THEN I WANT
YOU TO CALL ME,
BY PRESSING #9.
SO YOU'RE GOING TO
LIFT UP YOUR RECEIVER,
AND YOU'RE GOING
TO PRESS #9,
AND YOU'RE GOING TO ANSWER
A PARTICULAR QUESTION:

A blue slate under the title “Fibonacci Sequence (Infinite sequence) appears. It reads “The first twelve Fibonacci numbers are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.”

Lorraine continues BY LOOKING AT
THIS SEQUENCE,
CALL ME BY PRESSING #9
AND SHARE WITH ME,
WHAT ARE YOU NOTICING
ABOUT THIS SEQUENCE?
HOW DO WE GET TO
THE NEXT NUMBER?
WHAT ARE WE DOING?
AND I CAN SEE A FEW
OF YOU'RE CALLING IN.
THIS IS GREAT.
I'LL LET THE OTHERS HAVE
A FEW MORE MINUTES
TO LOOK AT IT.
AND I'M ALSO ABLE TO
PUT UP MY PICTURE HERE
IN THE CORNER.
AND THIS WAY, WHEN I'M
ABLE TO TALK TO YOU,
I'M GOING TO CALL...
JOHN.
AND IF YOUR PHONE
IS RINGING, JOHN.
OKAY, AS YOU
CAN TELL HERE -
I ALSO HAVE ACCESS
TO A POINTER.
AND HERE WE GO.
I'VE GOT TO
CLEAR THAT.
ONE MOMENT.
OKAY, AND THE
TELESTRATER HERE,
AS I'M PUTTING IT ON,
OKAY, THERE WE GO.
SO IF I WANT TO HAVE A
LITTLE BIT OF FUN HERE,

The computer cursor appears on the screen, and Lorraine draws on herself.

Lorraine says I'M ABLE TO ADD A
LITTLE MORE HAIR,
AS WE NOTICE
HERE, ON MYSELF,
AND THEN I CAN OBVIOUSLY
MOVE AROUND AND CLEAR THAT.
SO IF I WAS TO GO BACK
TO THE POWER POINT
I WAS SHOWING YOU
EARLIER, AND I WANTED
AN ILLUSTRATION OF
THIS, AN EXPLANATION.
I COULD THEN EXPLAIN
IT IN FURTHER DETAIL,
IF YOU ADD THESE TWO,
YOU GET THE NEXT NUMBER,
WHICH WOULD BE TWO.
AND THEN IF YOU ADD ONE
AND TWO, YOU GET THREE,
AND SO ON, AND I
ADDS ON FROM THERE.
ANOTHER EXAMPLE I WOULD
BE ABLE TO DO FOR THE
FIBONACCI, LET'S SAY, WE
SEE IT IN THE SEQUENCE,
SO ON, IN NATURE.
WE SEE IT IN
SPACE, IN MUSIC,
THE SEQUENCES ARE
ALL AROUND US.
ONE OF THEM BEING,
LET'S SAY IN NATURE,
WITH THE PINEAPPLE.

She shows a pineapple with eight dots following the pattern in a diagonal line.

Lorraine continues I COULD SHOW THE
STUDENTS HERE,
A PINEAPPLE WITH THE
DIFFERENT LAYERING.
THAT BY COUNTING THEM,
THERE ARE EIGHT.
AND THAT IS A
FIBONACCI NUMBER.
AS WELL, THE
SPIRALING EFFECT THAT
ONE CAN SEE WITH THE
GOLDEN RECTANGLES.
AND I COULD BRING
THAT UP CLOSER.

She shows a drawing of a spiral drawn in a set of Fibonacci rectangles.

Lorraine continues HERE ARE MANY GOLDEN
RECTANGLES WITH,
ONCE AGAIN, THE FIBONACCI
NUMBERS BEING ONE,
TWO, AND THEN
GROWING FROM THERE,
AND IF WE ADD AN ARC TO
ALL THE GOLDEN RECTANGLES,
WE SEE, THEN, THE
SPIRAL EFFECT,
WHICH ARE IN MANY OF
THE ANIMALS
SUCH AS THE SNAIL,
AND SO ON.

She shows a drawing of a snail shell with a spiral pattern.

Lorraine continues AND AS WELL, I'M ABLE TO
SHOW YOU ANOTHER EXAMPLE,
LET'S SAY, IN NATURE, OF
THE FIBONACCI NUMBERS,
BY SHOWING YOU
A LITTLE VIDEO.
AND IF YOU GUESS
WHAT THAT IS.

A clip shows a sunflower.

Lorraine says AND IF YOU GUESSED
A SUNFLOWER,
YOU'RE VERY
MUCH CORRECT.
AND THEY'VE NOTICED, AS
WELL, IN THE SUNFLOWER,
THERE ARE MANY SPIRALS THAT
GO COUNTER CLOCKWISE,
AS WELL AS SOME
THAT GO CLOCKWISE.

She draws lines following the spiral pattern of the sunflower.

Lorraine continues AND AGAIN, THE DIFFERENT
COLUMNS ALWAYS RELATE
TO NUMBERS IN THE SEQUENCE.
SUCH AS 34, AND 55.
AND ONCE AGAIN, I'M
ABLE TO CLEAR THAT.
AND I ALSO HAVE ACCESS,
IF I WERE TO HAVE A GUEST
IN HERE TO EXPLAIN
EVEN FURTHER ABOUT
FIBONACCI NUMBERS BECAUSE AS
I'M SURE YOU'RE ALL AWARE,
INTERNATIONALLY, IN 13
DIFFERENT COUNTRIES,
THERE'S 50 MATHEMATICIANS
THAT COME AROUND AND
MEET IN DIFFERENT AREAS OF
THE WORLD TO TALK ABOUT
FIBONACCI NUMBERS.
SO LET'S SAY I
HAD ONE HERE,
I WOULD THEN BE ABLE TO
HAVE A GUEST CAMERA,
LET'S SAY, RIGHT
NEXT TO ME,
WHICH IS WHAT THEY ARE
PLAYING WITH RIGHT NOW.
OR IT COULD BE THE
TWO OF US TOGETHER
I CAN HAVE ACCESS TO.
I CAN HAVE ONE
TO JUST MY GUEST.
AND I CAN PLAY
WITH THAT, AS WELL.
AND ALSO, AS YOU NOTICED
EARLIER, THERE'S A TABLE,
AND THAT'S OFF
TO ONE SIDE,
IF WE WANTED TO
DO AN EXPERIMENT,
DEMONSTRATING SOMETHING,
WE'RE ABLE TO DO THAT
BY HAVING THE CAMERA
AT THAT ANGLE.
AND FROM A TEACHER'S
PERSPECTIVE,
IT'S VERY EXCITING.
WHAT'S NICE IS YOU HAVE
A LOT OF TEAM EFFORT.
IF I'M WANTING SOMETHING
ON A PARTICULAR VIDEO,
I'M ABLE TO ACCESS IT THROUGH
SOMEONE AT TV ONTARIO.
THE DIFFERENT THINGS AS
WELL WITH THE ORAL SYSTEM
IS I'M ABLE TO
ASK QUESTIONS,
AND SO ON, WHERE YOU CAN
ANSWER WITH YOUR PHONES.
AND THIS WAY,
THROUGH THE DATABASE,
I'M ABLE TO SEE HOW
WELL YOU'RE ANSWERING,
IF YOU'RE HAVING
ANY DIFFICULTIES,
AND I CAN OBVIOUSLY
HELP OUT IN THAT SENSE.
AS WELL, THERE ARE VIRTUAL
FIELD TRIPS ONE CAN DO.
WE CAN GO OUT TO THE ROM;
JUST THE OTHER DAY
WE WENT TO IRWIN TOYS TO
DISCUSS SOMETHING FOR
THE SCIENCE AND TECHNOLOGY
PROGRAM WITH THE DESIGNERS.
AND I'M NOT TOO SURE
WHAT TO ADD THERE.
ARE MANY, MANY
DIFFERENT FACETS.
IT'S VERY EXCITING.
I BELIEVE IF YOU'RE
ABLE TO TRY IT OUT,
AND EVEN COME IN HERE AND
SEE WHAT WE'RE ABLE
TO ACCESS, AND SO ON, IT
GETS TO BE QUITE EXCITING.
...SAMPLES SO YOU CAN
SEE WHAT IT IS EXACTLY
WE'RE ABLE TO DO.
SO IT'S A TYPE OF DEMO,
AND YOU'LL HAVE
ACCESS TO THAT.
AND IF YOU HAVE ANY
QUESTIONS AFTER THAT,
WE'LL TRY AND
HELP YOU OUT.
HERE WE GO.

A clip shows a black screen with a caption that reads “Virtual Classroom Program Sample. (Spring 1998).”

A man in his forties appears. He is clean-shaven, has short brown hair, and is wearing a dark blue shirt and glasses.
He is standing in front of a table with several water filled glass tubes, and is holding a bottle with a red liquid in his hand.

The man says I'M GOING TO DO SOME
DEMONSTRATIONS WITH
A SUBSTANCE CALLED A
UNIVERSAL INDICATOR.
AND THAT'S IT
RIGHT HERE.
IT'S, IN FACT, A
MIXTURE OF A NUMBER
OF DIFFERENT INDICATORS.
LET'S SEE WHAT IT DOES.

A caption appears on screen. It reads “OAC Chemistry.”

A woman narrates THE VIRTUAL CLASSROOM
OFFERS A WIDE RANGE OF
EDUCATIONAL
OPPORTUNITIES.
WE CONNECT STUDENTS
TO THE CURRICULUM.

A clip various rock formations inside a cave.

The woman continues OAC CHEMISTRY, WITH
INSTRUCTOR, DON PLUM,
IS A CREDIT COURSE
OFFERED THROUGH
THE INDEPENDENT
LEARNING CENTRE.
ORIGINALLY A
CORRESPONDENCE COURSE,
DON HAS MADE IT MORE
VISUALLY APPEALING AND
INTERACTIVE FOR STUDENTS.
IT APPEALS TO STUDENTS
WHO NEED TO UPGRADE,
PART-TIME STUDENTS, OR
THOSE SCHOOLS THAT CAN'T
OFFER THE COURSE
IN ANY OTHER WAY.

A clip shows Don sitting at a desk with a computer and several papers and books in front of him.

Don says HI, IS JACOB THERE?

Jacob says HI.

Don says HOW ARE YOU?

Jacob says I'M OKAY.

Don shows a chemistry problem: “Cave Formation. What are the missing substances? Limestone CaCO3(s) – Ca(HCO3)2(aq) + [blank](l) calcium + [blank](g) bicarbonate solution.”

Don says LET'S JUST LOOK AT
THIS ONE RIGHT HERE.
THERE WERE TWO MISSING
SUBSTANCES HERE.
CAN YOU TELL ME,
PERHAPS, WHAT THE LIQUID
WAS THAT WOULD BE REQUIRED
TO BALANCE THIS EQUATION?

Jacob says H20.

Don says ABSOLUTELY.
WATER IS REQUIRED.
SO H20 IS THE
SUBSTANCE.
THE GAS IS A LITTLE
MORE DIFFICULT.
IT'S NOT NEARLY AS OBVIOUS
WHAT THE GAS WOULD BE.
ANY GUESS AT
WHAT THE GAS WAS?

Jacob says CO2.

Don says IT IS.
OKAY, THAT'S TERRIFIC.

A clip shows a large building with a dome.

The woman continues MORE OFTEN, OUR
CURRICULUM SESSIONS
ARE ENHANCEMENTS TO
WHAT IS ALREADY
BEING TAUGHT IN
THE CLASSROOM.

A clip shows a man and a woman standing on the terraces of a basketball stadium.

He says WE'RE UP IN THE 500 LEVEL
OF THE SKYDOME ARCHWAY.

She says YES, WE ARE.

He says WE'VE GOT A GREAT VIEW OF
THE FIELD FROM UP HERE.
JUST HOW BIG IS THAT
FIELD DOWN THERE?

She says IT'S ACTUALLY 13,300
SQUARE METRES.

He says OH, THAT'S
SOMETHING ELSE.
BUT I HAVE A LITTLE
BIT OF DIFFICULTY
GETTING A HANDLE ON
JUST HOW BIG THAT IS.
HOW ABOUT AIRPLANES?
WHAT ABOUT, 747s?
HOW MANY 747s COULD
YOU GET DOWN THERE?

She says YOU COULD FIT EIGHT
747s ON THE FIELD.

He says OH, THEY'RE HUGE, TOO.
I CAN JUST
IMAGINE THAT.
WHAT IS THAT?

A clip shows a huge screen on a wall.

She says THAT'S OUR JUMBOTRON.
JUMBOTRON IS ONE OF THE
WORLD'S LARGEST VIDEO BOARDS.

He asks HOW BIG IS IT?

She says IT'S 10 METRES
BY 33.5 METRES.

He says IT'S MADE UP OF A WHOLE
BUNCH OF LITTLE LIGHTS.
CAN YOU TELL ME
HOW MANY THERE ARE?

She says THERE ARE EXACTLY
67,200 TRINI LIGHTS.

He says YOU KNOW SOMETHING, I
THINK THAT'S THE MAKING
OF A MATH PROBLEM FOR
THIS VIRTUAL CLASSROOM.
THANK YOU VERY MUCH FOR
HELPING ME OUT TODAY.

A woman narrates TEACHERS, STEWART CRAVEN,
AND LORRAINE GOWER,
TEAM UP TO DELIVER AN
EIGHT-PART MATH MYSTERY,
USING CLUES AND
ACTIVITIES ALIGNED
WITH THE NEW ONTARIO
MATH CURRICULUM.

A clip shows Lorraine sitting at a desk with Stewart. He is in his thirties, has a brown full beard and brown hair, and is wearing a white T-shirt, a black cap and glasses.

Lorraine says THAT'S THE BEAUTY OF
INTERACTIVE TELEVISION.
WE'RE GOING TO ASK
YOU A QUESTION,
AND YOU DO NEED
YOUR PHONES.
AND THE ANSWER WAS
SAID IN THE VIDEO.

A blue slate appears under the title “Question No. 2.” It reads “How many Trinilights in the Jumbotron? 1. 1240; 2. 32600; 3. 67200; 4. 224000.”

A clip shows a man and a woman on a stage. They have blood on their hands and faces.
A caption reads “Shakespeare.”
[knocking]

The woman says I HEAR KNOCKING
AT THE SOUTH ENTRY.
RETIRE WE TO
OUR CHAMBER.
A LITTLE WATER CLEARS
US OF THIS DEED.

A woman narrates OTHER CURRICULUM
SESSIONS TAKE ADVANTAGE
OF OUR TELEVISION
PRODUCTION RESOURCES,
LIKE THIS SERIES OF
SHAKESPEARE DRAMATIZATIONS,
SPECIFICALLY SHOT FOR USE
IN THE VIRTUAL CLASSROOM,
AND INTRODUCED TO STUDENTS
BY THEATRE EXPERT,
RICHARD OUZOUNIAN.

A clip shows Richard sitting at a desk. He is in his forties, clean-shaven, with short brown hair. He is wearing a red shirt, striped black and yellow tie, and glasses.

Richard says ONE OF THE THINGS PEOPLE
ALWAYS TALK ABOUT
WITH
MACBETH
IS LOOKING AT,
IS IT JUST ABOUT GUILT,
OR IS IT ABOUT
MORE THAN GUILT?
NOW, STUDENT THREE,
COLLEGE AVENUE,
HAVE YOU ON THE LINE?

Student three says YEAH.

Richard says GOOD MORNING.
WHAT DO YOU THINK IS
BEHIND LADY MACBETH'S
OBVIOUS DISTRESS
IN THIS SCENE?
IS IT JUST GUILT, OR IS THERE
SOMETHING MORE THAN THAT?

Student three says I THINK SHE'S KIND OF
GOING MAD BECAUSE
SHE THINKS PEOPLE ARE
GOING TO FIND OUT,
OR SHE'S GOING TO BE
KILLED OR SOMETHING
BECAUSE SHE
KILLED THE KING.

Richard says SO YOU THINK SHE'S
WORRIED ABOUT
PRACTICAL CONSEQUENCES.

A clip shows a man rotating two plastic gears.

The woman continues THE VIRTUAL CLASSROOM IS
ALSO AN IMPORTANT VEHICLE
FOR PROFESSIONAL
DEVELOPMENT.
WORLD IS MOTION IS A CROSS
CURRICULAR TECHNOLOGY
PROJECT FOR
INTERMEDIATE GRADES,
CREATED BY THE SOCIETY
OF AUTOMOTIVE ENGINEERS.

The man says AS I ROTATE THIS
AROUND ONCE, TWICE.

The woman continues OVER EIGHT SESSIONS,
TEACHER MARTIN GABBER
INTRODUCES THE
TECHNOLOGICAL CONCEPTS AND
KIT CONTENTS TO TEACHERS
TO HELP THEM CARRY OUT
THE PROJECT IN THEIR
OWN CLASSROOMS.

A clip shows Martin sitting at a desk. He is in his forties, clean-shaven with short dark brown hair. He is wearing a white shirt and purple tie.

Martin says THERE'S LOTS OF GOOD
SUPPORT AREAS FOR ALL
OF THIS, AND ONE OF THE
SUPPORT AREAS COMES
FROM THE ONTARIO SOFTWARE
ACQUISITIONS PROGRAM.
AND IT'S THIS CD
ROM RIGHT HERE,
AND IT'S CALLED THE
WAY THINGS WORK.
HERE WE COME INTO THE
MAIN SCREEN RIGHT HERE,
WHICH IS THE A
TO Z OF MACHINES.
IF WE GO TO G, WE CAN
GO TO GEARS RIGHT AWAY.
AND THERE WE SEE
GEAR DERAILLEUR.
AND THERE ARE ALL
KINDS OF THINGS HERE.
HERE'S A GOOD EXAMPLE,
THIS LINKS UP VERY
WELL WITH THE PREVIOUS
HOMEWORK EXERCISE ON GEARS.

A clip shows Lorraine sitting with a man at a desk. There are several toys in boxes on the desk.

The woman continues THEN, LORRAINE GOWER
WORKS WITH THE STUDENTS
AS THEY BEGIN TO CREATE
MECHANIZED TOYS.
HERE, SHE INVITES A TOY
MANUFACTURER INTO THE STUDIO.

The man says SO WE CAME UP WITH
ANOTHER IDEA WHERE
WE'D TAKE THE BLACK OUT,
AND WE LEAVE THE YELLOW
BORDER FOR
NATIONAL
GEOGRAPHIC

He shows a stuffed Kangaroo in a National Geographic themed box.

The man continues BUT WE'D PUT THE KANGAROO
IN HIS HABITAT.
SO WE'VE GOT A GRASSLAND
IN BEHIND HIM,
INSTEAD OF THE BLACK
WE STARTED OUT WITH.

Lorraine says OH, YES, YOU DO
SEE A DIFFERENCE.

The man continues SO YOU CAN SEE HOW
THERE'S BEEN
AN IMPROVEMENT
FROM THE HANG TAG,
WHICH NOBODY COULD SEE,
TO THE BOX WITH THE BLACK
BACKGROUND, AND NOW
FINALLY WHERE WE'RE AT TODAY.

A clip shows a classroom with several students sitting in a circle.
A caption reads “Galaxy Professional Development.”

The teacher says SO WE HAVE PUT STEPHANIE
IN THE HOT SEAT.
AND SHE'S GOING TO
BE OLIVER BUTTON.

A girl reads a sheet of paper HOW DID YOU FEEL WHEN
YOUR PARENTS PUT YOU
IN THE DANCE CLASS?

A woman narrates THE GALAXY PROJECT IS A
HANDS-ON, INQUIRY-BASED,
MODEL CURRICULUM FOR
ELEMENTARY TEACHERS.
AS ONE COMPONENT
OF THE PROJECT,
THE VIRTUAL CLASSROOM IS
USED TO BRING TOGETHER THE
PARTICIPATING TEACHERS
ON A REGULAR BASIS,
AND OFFER ADDITIONAL
TRAINING.

A clip shows two women sitting at a desk with a computer. One is wearing a blue blazer, and the other is wearing a black blazer.

The woman in blue says HI, TERRY.

Terry says GOOD MORNING.

The woman in blue says GOOD MORNING.
AND SUSAN, DO WE
STILL HAVE YOU?

Susan says YES.

The woman in blue says GREAT.
TERRY, GO AHEAD AND ASK
SHILOH SOME QUESTIONS.

Terry says SURE.
HI, SHILOH.

Shiloh says HELLO.

Terry asks CAN YOU DESCRIBE TO
ME WHAT YOU LOOK LIKE?

Shiloh says UM, WELL, I'M
A HUNTING DOG,
SO I'M BROWN AND WHITE,
AND I HAVE LONG EARS.
AND I HAVE A
LONG, LONG, TAIL.

A clip shows numerous students in a school gym.
A caption reads “Math Adventure.”

A woman narrates THE VIRTUAL CLASSROOM
CAN TAKE PARTICIPANTS
TO PEOPLE AND PLACES
OUTSIDE TV ONTARIO.
STEWART CRAVEN,
OUR MATH EXPERT,
WAS ON SITE AT A LOCAL
ELEMENTARY SCHOOL,
TO ANSWER TEACHERS'
QUESTIONS ABOUT PLANNING
A MATH ADVENTURE
PLAY DAY.

A woman says HELLO, FRANCES.

Frances says HI, HOW ARE YOU?

The woman says FINE.
WHAT'S YOUR QUESTION
FOR STEWART?

Frances says MY QUESTION IS, HOW
OFTEN WOULD YOU RUN
A PLAY DAY LIKE THIS?
ONCE A TERM WOULD
BE SUFFICIENT?

Stewart asks YOU MEAN THE
ELEMENTARY SCHOOL?

Frances says YES.

Stewart says IF WE RAN A MATH
ADVENTURE DAY AT
AN ELEMENTARY SCHOOL
ONCE A YEAR,
I THINK I'D BE
REALLY THRILLED.
BECAUSE YOU REALLY DO
NEED - IT'S A LOT OF WORK
FOR THE HIGH
SCHOOL CLASS.
IT'S PROBABLY A LITTLE
BIT EASIER ON THE STAFF
AT THE ELEMENTARY SCHOOL
BECAUSE THE HIGH SCHOOL CLASS
IS SUPPOSED TO BRING IN
ALL OF THE MATERIALS.
BUT IT'S A MAJOR
UNDERTAKING FOR THOSE
HIGH SCHOOL STUDENTS.

A woman narrates WE CAN ALSO BRING SPECIAL
GUESTS INTO THE VIRTUAL
CLASSROOM STUDIO.
OUR OLYMPIC EVENTS ALLOWED
STUDENTS TO SPEAK WITH
ATHLETES THEY WOULDN'T
OTHERWISE CONNECT WITH,
LIKE GERALDINE HEANEY,
AND VICKY SUNOHARA,
TWO MEMBERS OF THE
CANADIAN WOMEN'S OLYMPIC
HOCKEY TEAM.

A clip shows three women sitting at a desk. A caption reads “Olympic Special.”

A woman says I HAVE A QUESTION
FOR BOTH OF YOU.
HOW DOES IT FEEL TO BE THE
FIRST WOMEN'S HOCKEY TEAM,
AND ACHIEVE
WINNING A SILVER MEDAL?

Geraldine says JUST PARTICIPATING
IN THE OLYMPICS
WAS A DREAM COME
TRUE FOR BOTH OF US.
AND LIKE I SAID BEFORE,
WINNING THE SILVER MEDAL,
AT THE TIME, WAS PROBABLY
A DISAPPOINTMENT,
BUT IT'S THE GREATEST THING
THAT'S EVER HAPPENED TO ME
AND JUST PARTICIPATING
IN THE OLYMPIC GAMES
IS A DREAM COME TRUE.

(music plays)

A white slate appears with the title “tvo’s Virtual Classroom. Get Connected.”

A clip shows Lorraine sitting at a desk with a man in his forties. He is clean-shaven, has short black hair, and is wearing a white shirt and a green tie.

Lorraine says GOOD AFTERNOON.
WE'RE VERY FORTUNATE HERE
IN THE VIRTUAL CLASSROOM
TO HAVE GOPAL WITH US.
WELCOME TO THE
VIRTUAL CLASSROOM.

Gopal says GOOD AFTERNOON.
OR GOOD EVENING,
WHATEVER TIME IT IS.

Lorraine says THAT'S RIGHT.
AND JUST WANT TO
EXPLAIN TO YOU,
ABOUT THE QUESTRON,
AS YOU WERE NOTING,
IF YOU WANT TO PLAY A
LITTLE BIT, ANY TIME,
PLEASE LET ME KNOW.

Gopal says OKAY.

Lorraine continues SO YOU WERE MENTIONING
JUST EARLIER YOU'RE
WANTING TO MAYBE CONSIDER
THIS PROGRAM IN INDIA.
DO YOU WANT TO TELL US
A LITTLE BIT ABOUT IT?

Gopal says SURE.
WE'RE DOING THIS PROGRAM
CALLED SCHOOL INDIA,
WHERE WE'RE GOING TO
LINK A HUNDRED SCHOOLS
IN A PILOT PROJECT.
AND WE WANT TO SEE WHAT
WE CAN DO WITH VIDEO
AS THE INITIAL CONTENT.
IT'S MUCH EASIER
TO HANDLE.
TEACHERS CAN DEAL WITH
IT IN A MUCH MORE
USER FRIENDLY WAY,
RATHER THAN COMPUTERS.
SO THAT'S ONE OF
THE INTERESTS.

Lorraine says OKAY.

Gopal says QUITE FASCINATED WITH THE
NUMBER OF GIZMOS YOU HAVE.

Lorraine says THAT'S RIGHT.

Gopal says I WANT TO CHANGE PLACES
WITH YOU SOME TIME.

Lorraine says RIGHT NOW, IF I GO
TO THE HOST CAMERA,
THAT'S THE TWO
OF US AS YOU SEE.
SO IF YOU WANT, PRESS
THE GUEST RIGHT NOW.

Gopal says OKAY.

Lorraine says AND YOU WILL NOTE
NOW THE RED LIGHT.
SO YOU'RE THE GUEST.
AND IF YOU LOOK AT
YOURSELF RIGHT NOW ON
THE SCREEN, SEE HOW YOUR
EYES ARE NOT LOOKING AT US.

Gopal says I'VE GOT TO LOOK
AT THE CAMERA.

Lorraine says EXACTLY.
WHEN YOU LOOK AT
THE RED LIGHT,
IT'S NICE AND CENTRAL, SO
YOU'RE TALKING RIGHT NOW.
AND LET'S SAY IF I WANT
TO COME BACK AND ASK YOU
ANOTHER QUESTION,
I PRESS THE HOST,
AND THAT MEANS THE TWO OF
US, I ASK YOU A QUESTION.

Gopal says AND WE COULD
TALK LIKE THIS.

Lorraine says THAT'S RIGHT.
AND IF YOU WERE TO ANSWER
AGAIN, I COULD DO THIS.

Gopal says WOW.
CAN YOU SHOW ME
THE PREVIEW STUFF?
CAN I SEE THAT AGAIN?

Lorraine says PARDON?

Gopal repeats THE PREVIEW?

Lorraine says SO FOR INSTANCE, IF I
GO TO GUEST RIGHT HERE,
I CAN PLAY WITH
THE CAMERA.
SEE HOW I'M
BRINGING YOU IN?

Gopal says OKAY.

Watch: Student Session 16