▌MathLove MathTool ▌Pythagorean Puzzle Set
– 5 Types
▄ Curriculum : Pythagorean Proof
▄ Components : 5 types of Pythagorean puzzle set
▄ Purpose
Pythagorean Puzzle understands teaching tool for
Pythagoras’ s theorem, with puzzle piece.
Put in puzzle piece each different regular quadrilateral
To understand Pythagorean’s theorem with this puzzle, place the pieces appropriately into the
puzzle. Also, a better understanding of mathematical theories will result with these puzzles. A
better understanding of proof of theories will result by just playing with them. Instead of
calculating abstract numbers, you can actually see and play with the puzzles to understand it.
▄ Dimension : Width 187mm × Length 215mm
▄ About Pythagorean Theorem
In a down triangle, the sum of the squares of the lengths of the sides is equal to the square of
the length of the hypotenuse.
c
b
a2＋b2 = c2
a
“The Pythagorean theorem , or the Pythagoras’s theorem - perhaps the most renown or all
mathematical theorems - was known by the Babylonians as far back as 2000 B.C., that is,
about 1500 years before the time of Pythagoras and Pythagorean.”
Reference: Jan Gullberg. Mathematics
From the Birth of Numbers. W.W.NORTON&COMPANY.
Gullberg page 435. 1997.
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▄ A method of rearranging congruent rectangles
Pythagoras Theorem A – Pythagoras’ Proof
How did Pythagoras prove the “Pythagorean Theory”?
Many
people believe that Pythagoras arrived at his theory by the
tiles that were spread out on the floor. However, we assure
you that he must have gone through the following process for
the proof. If nine 1 × 1 squares are added to one 4 × 4 square
as illustrated, a 5 × 5 square is created. Similarly, another sized
3² + 4²
5²
square is made if a clamp shape is added to any squares.
▄ A method of moving a square by partition
In any right-angled triangle, the square on the hypotenuse is equal to the sum of the squares
on the other two sides. This can be considered to be a modification of Euclid’s method. It
will be as fun as solving a puzzle.
Pythagoras theorem B - Perigal’ s Proof
Henry Perigal was a stockbroker and amateur astronomer. In 1830, he announced a single,
elegant proof of the Pythagoras theorem.
Locate the center of the middle-sized square. Call it A. Through A draw
a line parallel to the hypotenuse and then a line through A perpendicular
to the hypotenuse (as illustrated).
Cut out shapes 1, 2, 3, 4, 5 and 6.
Try to fit 1, 2, 3, 4 and 5 on 6, thus
verifying the theorem of Pythagoras. This construction is
known as Perigal's dissection.
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Pythagoras theorem C - Campa’ s Proof
□ ACGF= □ JDLK=□ EONM
MP // DB ,
KQ // LM
The seven pieces, combined with 5 pieces of
the square AEDB and 2 pieces of the square
JDLK, can fit on the square BCIH.
Pythagoras theorem D - Baskara’ s Proof
Draw three squares so that each of them
contains a different side of a rightangled triangle ABC. Through C, draw
a line (PR) parallel to the hypotenuse
(AB).
Try to fit the five pieces on
the big square (ABHI) thus verifying
the theorem of Pythagoras
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Pythagoras theorem E - Lui Hui’ s Proof
Lui Hui’s proof was introduced by a 9-paged arithmetic paper. (It
is composed of the nine pages related to a right-angled triangle
and contains 24 questions with algorithms.) It was from the third
century.
Draw a diagonal line to the square ABDE in order to divide it into
two pieces.
After drawing a
square FPRQ (FP=AC-AB),
draw a line CP, CQ, CR in order to divide it into five
different pieces.
The seven pieces, combined with two pieces of the
square ABDE and five pieces of the square ACGF, can fit
on the square BCHI.
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