## Contributions to Math

Leonardo Da Vinci was a true renaissance man. He had many interests; therefore he had many contributions in many different subjects. He had contributions in math, art, science, biology, and more. It has been revealed that Da Vinci studied hydraulics the most according to his notebook. Da Vinci made the first empirical studies of streams and their velocity distribution. His methods of proving his theories were complicated, but accurate, and were very extreme. (www.waterencyclopedia.com)

While Da Vinci was working for the Duke of Milan, he had a lot of time to observe nature. He became an expert on geology (rocks and minerals). He was interested in the idea of moving mountains and putting a tunnel through them. In his notebook, this he labeled as the study of sedimentation. He was the one who explained that the sedimentation in water could erode the rocks. (www.waterencyclopedia.com)

Da Vinci also made many military weapons. It was said that he was told to design them since he was a painter. He also designed some topographical maps. Da Vinci has also made a flying machine, researched the flight of birds, and has tried to square a circle. (www.yankeegardener.com)

He is also a painter. He used math in his paintings though. He used something called the golden ratio, when he painted. It was something to help him with his portraits, and something to help him be symmetrical. (www.mathematicianspictures.com)

The golden ratio is basically Fibonacci’s sequence. The golden ratio (or golden mean or golden rectangle) is a number that is equal to almost 1.6180339887498948482. You would use the Greek letter Phi for this ratio. Like Phi, the golden ratio can go on forever without any numbers repeating.(http://mathforum.org/dr.math/faq/faq.golden.ratio.html)

Da Vinci used the concept of Fibonacci’s Golden Ratio for his paintings. He used the golden rectangle for his

While Da Vinci was working for the Duke of Milan, he had a lot of time to observe nature. He became an expert on geology (rocks and minerals). He was interested in the idea of moving mountains and putting a tunnel through them. In his notebook, this he labeled as the study of sedimentation. He was the one who explained that the sedimentation in water could erode the rocks. (www.waterencyclopedia.com)

Da Vinci also made many military weapons. It was said that he was told to design them since he was a painter. He also designed some topographical maps. Da Vinci has also made a flying machine, researched the flight of birds, and has tried to square a circle. (www.yankeegardener.com)

He is also a painter. He used math in his paintings though. He used something called the golden ratio, when he painted. It was something to help him with his portraits, and something to help him be symmetrical. (www.mathematicianspictures.com)

The golden ratio is basically Fibonacci’s sequence. The golden ratio (or golden mean or golden rectangle) is a number that is equal to almost 1.6180339887498948482. You would use the Greek letter Phi for this ratio. Like Phi, the golden ratio can go on forever without any numbers repeating.(http://mathforum.org/dr.math/faq/faq.golden.ratio.html)

**1 + sqrt{5}****------------****2**Da Vinci used the concept of Fibonacci’s Golden Ratio for his paintings. He used the golden rectangle for his

__Mona Lisa__’s face. In his work of__the Last Supper,__he used the golden ratio to get the positions of where people were sitting and for the ceiling. For his statue of Athena, he noticed that if the human head is turned sideways illustrates the golden ratio. (http://library.thinkquest.org)