The document discusses the Fibonacci sequence and its use in art and architecture. The Fibonacci sequence is a series of numbers where each subsequent number is the sum of the previous two. Leonardo Da Vinci and other artists like Johannes Vermeer and Michelangelo used the proportions of the Fibonacci sequence and the golden ratio in their famous works like the Mona Lisa, The Last Supper, and The Creation of Adam to achieve harmonious and aesthetically pleasing compositions. Architects also employed the Fibonacci sequence and golden ratio principles in the design of landmarks such as the Eiffel Tower and Taj Mahal.

1. MATHEMATICS IN ART
Group 5

2. FIBONACCI SEQUENCE
Fibonacci sequence - a sequence of
natural numbers determined
recursively as follows: The first term
is equal to 0, the second term is
equal to 1, each subsequent term is
the sum of the previous two.

3. WHY DOES IT EXIST?
Fibonacci numbers and the golden ratio were also used in architecture
by the moderns, building, for example, the Eiffel Tower, Notre Dame
Cathedral or the Taj Mahal. It is thanks to the golden ratio that these
buildings are to be perceived as harmonious and perfect in their form.

4. FIBONACCI SEQUENCE IN ART
Leonardo da Vinci himself used the golden ratio to create his paintings,
such as: Mona Lisa, The Last Supper, The Birth of Venus or the marble
sculpture Venus de Milo. He used it to create the famous Vitruvian
Man whose body parts tend to follow the golden ratio.

5. MONA LISA -
LEONARDO DA VINCI

6. THE LAST
SUPPER-
LEONARDO
DA VINCI

7. Girl With A Pearl Earring -
Johannes Vermeer

8. The Creation of
Adam -
Michelangelo

9. BIBLIOGRAPHY
● https://www.google.com/imgres?imgurl=https%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fb%2Fbf%2FPascalTriangleFib
anacci.svg%2F300px-
PascalTriangleFibanacci.svg.png&tbnid=6EYzgHdrTu7jQM&vet=12ahUKEwiZ8orqnqf_AhVMvCoKHYgRB8cQMygAegUIARDIAQ..i&imgrefurl=https%3A%
2F%2Fpl.wikipedia.org%2Fwiki%2FCi%25C4%2585g_Fibonacciego&docid=Cs1gL_1vt8ohRM&w=300&h=150&q=ci%C4%85g%20fibonacciego&ved=2ah
UKEwiZ8orqnqf_AhVMvCoKHYgRB8cQMygAegUIARDIAQ
● https://www.google.com/search?q=ci%C4%85g+fibonacciego&source=lmns&bih=569&biw=1280&rlz=1C1CHZN_plPL944PL944&hl=pl&sa=X&ved=2ahUK
EwiZ8orqnqf_AhVMvCoKHYgRB8cQ_AUoAHoECAEQAA#:~:text=Ci%C4%85g%20Fibonacciego%20%E2%80%93%20ci%C4%85g%20liczb%20naturalny
ch%20okre%C5%9Blony%20rekurencyjnie%20w%20spos%C3%B3b%20nast%C4%99puj%C4%85cy%3A%20Pierwszy%20wyraz%20jest%20r%C3%B3w
ny%200%2C%20drugi%20jest%20r%C3%B3wny%201%2C%20ka%C5%BCdy%20nast%C4%99pny%20jest%20sum%C4%85%20dw%C3%B3ch%20pop
rzednich.
● https://boringowl.io/blog/ciag-
fibonacciego#:~:text=Liczby%20Fibonacciego%20i%20z%C5%82ot%C4%85%20proporcj%C4%99%20wykorzystywali%20w%20architekturze%20tak%C5
%BCe%20nowo%C5%BCytni%2C%20buduj%C4%85c%20np.%3A%20wie%C5%BC%C4%99%20Eiffla%2C%20Katedr%C4%99%20Notre%20Dame%20
czy%20Tad%C5%BC%20Mahal.%20To%20w%C5%82a%C5%9Bnie%20dzi%C4%99ki%20z%C5%82otej%20proporcji%20budowle%20te%20maj%C4%8
5%20by%C4%87%20odbierane%20jako%20harmonijne%20i%20doskona%C5%82e%20w%20swojej%20formie.
● https://www.google.com/url?sa=i&url=http%3A%2F%2Fkonkursmat.opx.pl%2Fsztuka.html&psig=AOvVaw3abOAB2wMxSnZ0oZC5M34t&ust=1685887794
019000&source=images&cd=vfe&ved=0CBEQjRxqFwoTCPiEldCjp_8CFQAAAAAdAAAAABAE
● https://www.google.com/imgres?imgurl=http%3A%2F%2Fkonkursmat.opx.pl%2Fimages%2F25.jpg&tbnid=DF428-
o6FnLH5M&vet=12ahUKEwiyuoLKo6f_AhUGwyoKHd6-
C5IQMygGegUIARDLAQ..i&imgrefurl=http%3A%2F%2Fkonkursmat.opx.pl%2Fsztuka.html&docid=m0QxMxysQkD1mM&w=189&h=267&q=ci%C4%85g%2
0fibonacciego%20w%20sztuce%20OSTATNIA%20WIECZERZA&hl=pl&ved=2ahUKEwiyuoLKo6f_AhUGwyoKHd6-C5IQMygGegUIARDLAQ
● http://nostresskat.pl/wp-content/uploads/2020/05/mona-1.png
● http://nostresskat.pl/wp-content/uploads/2020/05/earing.jpg
● http://nostresskat.pl/wp-content/uploads/2020/05/dd99b09cd387fd5b6a23bbb44f8776cf.jpg

10. THANK YOU FOR YOUR
ATTENTION