educaiona

1. PC2 Enseny ament - Aprenentatge Pla lector mates 1ESO Versió
Data abril
2014
Elaborat : Departament de
Mates
Rev isat Aprov at Pàgina 1 de 5
The Sierpinski
triangle

2. PC2 Enseny ament - Aprenentatge Pla lector mates 1ESO Versió
Data abril
2014
Elaborat : Departament de
Mates
Rev isat Aprov at Pàgina 2 de 5
Waclaw Sierpinski was a
Polish mathematician. In
1919 he created his famous
Sierpinski triangle, which
shows that a figure can have
infinite perimeter but area
zero. This fact contradicts the
Euclidean geometry.
Open it:
http://www..com/Lab/
SierpinskiTriangle.ex
e

3. PC2 Enseny ament - Aprenentatge Pla lector mates 1ESO Versió
Data abril
2014
Elaborat : Departament de
Mates
Rev isat Aprov at Pàgina 3 de 5
WHAT DO YOU KNOW ABOUT W. SIERPINSKI?
CARD 1: FACTS ABOUT HIS LIFE AND HIS WORK
Waclaw Sierpinski was born on March 14, 1882, in Warsaw, Poland. In 1900 he
entered the University of Warsaw, graduating four years later after having been
awarded a gold medal for mathematics. From 1908 to 1914 Sierpinski lectured at
the University of Lvov, followed by three years at the University of Moscow. After the
end of World War I he returned to the University of Warsaw and spent the rest of his
career there. He founded, in 1920, together with Mazurkiewicz, the important journal
Fundamenta Mathematicae. During the Second World War, he continued working in
the “Underground Warsaw University”. He received honorary doctorates from ten
universities, was elected vice-president of the Polish Academy of Sciences, and was
awarded the scientific prize of the first degree in 1949. Sierpinski died in Warsaw on
May 14, 1969.
Sierpinski's most important mathematical work was in the areas of set theory, point
set topology, and number theory. He published over 700 papers and 50 books.
CARD 2: FACTS ABOUT HOW TO CREATE THE TRIANGLE
Iteration 0: We create an equilater triangle which side is a:
Iteration 1: We join the dots in the midle of each side and we have this picture:
Three red equilater triangles and just one in the middle, not painted.

4. PC2 Enseny ament - Aprenentatge Pla lector mates 1ESO Versió
Data abril
2014
Elaborat : Departament de
Mates
Rev isat Aprov at Pàgina 4 de 5
Iteration 2: We repeat the process on every triangle and we obtain the next figure:
And so on.

5. PC2 Enseny ament - Aprenentatge Pla lector mates 1ESO Versió
Data abril
2014
Elaborat : Departament de
Mates
Rev isat Aprov at Pàgina 5 de 5
QUESTIONS
 EXPLICIT
Q1: Where was W. Sierpinski born? City, Country, language, ….
Q2: What was “Fundamenta Mathimaticae”?.
 IMPLICIT
general
Q3: The Second World War, what do you know about it? Years, main characters,
countries and alliances,…
about the construction
Q4: Could you write the instruction to do the iteration 3?
Q5: How many triangles have you created after this iteration?
 REFERENCIAL
about numbers:
Q6: Could you continue the sequence of numbers2 of triangles you obtain?
Q7: Could you recognize some property about the sequence? Multiples from?, power
of?…
Q8: It could be interesting to calculate the area of each triangle you obtain. Iteration 1,
2, 3
Q9: Also to calculate the global area obtained after the third iteration.