scribed in such a triangle and their sides are algebraically calculated In 1225 Leonardo completed his third book, Flos. In this book Leonardo included the challenge he had accepted from the Holy Roman Emperor Fredrick II. He listed the problems involved in the challenge along with the solutions. After completing this book he mailed it to the Emperor. Also in 1225, Leonardo wrote his fourth book titled Liber quadratorum. Many mathematicians believe that this book is Leonardo's most impressive piece of work. Liber quadratorum means the book of squares. In this book he utilizes different methods to find Pythagorean triples. He discovered that square numbers could be constructed as sums of odd numbers. An example of square numbers will be discussed in section II regarding root finding. In this book Leonardo writes:I thought about the origin of all square numbers and discovered that they arose from the regular ascent of odd numbers. For unity is a square and from it is produced the first square, namely 1; adding 3 to this makes the second square, namely 4, whose root is 2; if to this sum is added a third odd number, namely 5, the third square will be produced, namely 9, whose root is 3; and so the sequence and series of square numbers always rise through the regular addition of odd numbers. Leonardo died sometime during the 1240s, but his contributions to mathematics are still in use today. Now I would like to take a closer look at some of Leonardos contributions along with some examples. IIFibonaccis Contributions to MathDecimal Number System vs. Roman Numeral SystemAlgorithmRoot FindingFibonacci SequenceDecimal Number System vs. Roman Numeral System As previously mentioned Leonardo was the first person to introduce the decimal number system or also known as the Hindu-Arabic number system into Europe. This is the same system that we use today, we call it the positional system and we use base ten. This simpl...
