Infinite Surds (IB Math SL portfolio)

The first 200 words of this essay...

Infinite Surds

> Introduction to Infinite Surds

* Definition of a surd

- An irrational number whose exact value can only be expressed using the radical or root symbol is called a surd.

E.g.) is a surd, because the square root of two is irrational.

* The origin of the word

- In or around 825AD, Al-Khwarizmi who was an Arabic mathematician during the Islamic empire referred to the rational numbers as 'audible' and irrational as 'inaudible'. Then, the European mathematician, Gherardo of Cremona, adopted the terminology of surds (surdus means 'deaf' or 'mute' in Latin) in 1150. In English language, the 'surd' appeared in the work of Robert Recorde's The Pathway to Knowledge, published in 1551.

* The symbol, use of the word radical

- The radical symbol depicts surds, with the upper line above the expression called the vinculum. Also, a cube root takes the form, which corresponds to a1/3 when expressed using indices. So, all roots can remain in surd form.

* A definition of infinite surds

- An infinite surd is a never ending irrational number and its exact value would be left