(Music plays)

An animated clip shows a big orange X on a blue background. It explodes and letters and numbers come out of it in all directions and float around.

Mathemagician Eric appears on screen. He’s in his mid-twenties. He has short dark brown hair and a beard. He wears a red T-shirt with the show’s logo, blue jeans and red Tennis shoes.

The screen turns red and the logo of the show appears next. It reads "MathXplosion." Meanwhile, cones, cubes and dices float around it.

Kids voices sing a song with lyrics that go
WHAT A HIT
IT'S NOT A TRICK
IT'S MATHXPLOSION
JUST FOR YOU
COOL AND NEW
MATHXPLOSION!

The episode starts with Eric putting small fantasy trees in a box with sand.

Eric says HEY!
DID YOU KNOW THERE'S
A TRICK TO ARRANGING
FOUR OBJECTS SO THAT
THEY'RE EXACTLY
THE SAME DISTANCE
APART FROM EACH OTHER?
IF WE HAVE, LET'S SAY,
FOUR TREES TO PLANT,
HOW DO WE MAKE SURE EACH
TREE IS THE SAME DISTANCE
APART FROM EVERY
OTHER TREE?
THE SOLUTION MIGHT NOT
BE AS EASY AS YOU THINK.

(music plays)

He places a series of trees in the sand. Next, magically, he gets an apple.

Eric says LET'S DO SOME EXTRA
DIGGING TO FIND OUT
THIS ANSWER.
HEH HEH.

(music plays)

Eric is ready to start.

He says YOU MIGHT THINK A
SQUARE IS THE SOLUTION
BECAUSE SQUARES HAVE
FOUR SIDES AND WE HAVE
FOUR TREES.
GOOD IDEA, BUT NOPE.
THE TREES ARE THE
SAME DISTANCE APART
THIS WAY AND THIS WAY,
BUT THE TREES ACROSS
FROM EACH OTHER -
DIAGONALLY, HERE AND HERE -
ARE FURTHER APART.

A dynamic line forms a square connecting the four trees in the sand.

Eric says HMM.
HOW ABOUT
PUTTING ONE...
TWO...
THREE TREES IN
THE CORNERS
OF AN EQUILATERAL
TRIANGLE?

As he draws the triangle on the sand, the dynamic line traces it.

Eric continues
THAT'S A TRIANGLE WHERE
ALL THREE SIDES ARE
IN EQUAL LENGTH.
AND THE FORTH?
IN THE CENTRE ABOVE
THEM ALL ON A HILL.
ALL FOUR TREES WILL BE
THE SAME DISTANCE APART,
IF YOU THINK ABOUT IT
IN THREE DIMENSIONS
INSTEAD OF TWO.
TOGETHER, THEY
MAKE A TETRAHEDRON,
A PYRAMID WITH AN
EQUILATERAL TRIANGLE
FOR THE BASE.

He takes a triangular green structure and places it over the mark he previously made on the sand.

He says WHICH MEANS ALL FOUR
CORNERS ARE THE SAME
DISTANCE FROM
EACH OTHER.

(music plays)

He fills the whole structure with sand and forms a pyramid. Now he places a tree in every angle and one on top.

Eric says WE KNOW THESE STRAWS
ARE ALL THE SAME LENGTH,
SO WE KNOW EACH EDGE
OF THE TETRAHEDRON
IS THE SAME LENGTH.
WE ALSO KNOW THAT EACH
TREE IS EXACTLY THE SAME
DISTANCE FROM
ONE ANOTHER.
COOL.

(music plays)

Eric draws a circle and colours it inside. He taps on it and a new clip plays. The video shows a triangular shape rotating next to a pyramid. Both are spreaded out and the actual core shape gets revealed: the triangle uses a triangle and the pyramid uses a square.

Eric says AS I WAS SAYING,
A TETRAHEDRON IS
A TRIANGULAR PYRAMID.
IS IT LIKE THE ANCIENT
PYRAMIDS IN EGYPT,
YOU ASK?
NOPE, THERE ARE DIFFERENT
TYPES OF PYRAMIDS
AND THE EGYPTIAN ONES
ARE NOT TETRAHEDRONS.
THEY HAVE SQUARE BASES
AND FOUR TRIANGULAR FACES,
WHILE THE BASE OF A
TETRAHEDRON IS A TRIANGLE,
THE SAME AS
ITS OTHER FACES.
IF YOU LOOK HARD, YOU
CAN SEE TETRAHEDRONS
EVERYWHERE.

Eric appears back in the workroom.

He says SO, THINK IN 3-D.
YOU CAN DO IT WITH
TOYS, PLANTS...
WELL, ANYTHING,
REALLY.
MAKE A TETRAHEDRON AND
YOUR FOUR OBJECTS WILL BE
EXACTLY THE SAME
DISTANCE APART.
IT'S NOT MAGIC.
IT'S MATH.

He slowly disappears by getting down.

A big explosion brings the show’s logo back on the screen.

(music plays)

The end credits roll.

Produced by GAPC Entertainment in association with TVOKids.

Copyright GAPC Entertainment (MathPlosion) Incorporated, 2016.