# Algebra Geometry And Trigonometry

Key-Words: - Islam, Mathematics, Algebra, Geometry, Trigonometry

1 Introduction

Throughout time, cultures and societies have created and discovered amazing concepts that have been passed down and are now considered

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He went ahead and began by drawing a square having a side length ofx. In order to add 10x to the picture, he went ahead and drew four rectangles to each side measuring 5/2×x as we can see instep 2 of Fig. 2. In the last step, Al-Khwarizmi added small squares in the corners measuring 5/2× 5/2, therefore each having an area of 25/4 and completing the whole outside square. Taking a look at the final image, he was able to see that the area of the whole outside square could now be expressed as4×25/4+39=25+39=64. Knowing this, it can be concluded that the new side length of the square is 8 and the equation could be rewritten as 5/2+x+ 5/2=x+5=8. The final step for Al-Khwarizmi would be to solve the simple equation and conclude that

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Besides his discoveries and accomplishments in the areas of algebra and geometry, he also contributed to the area of trigonometry.

In reference [5], author Luke Mastin stated that, “The 13th Century Persian astronomer, scientist and mathematician Nasir Al-Din Al-Tusi was perhaps the first to treat trigonometry as a separate mathematical discipline.” Even though trigonometry was not viewed or treated as a separate subject until Al-Tusi did so, contributions to the area of trigonometry were made early on and before this time.

Al-Khwarizmi is also credited for making contributions to this area of mathematics. In reference [3], Khalid El Jafoufi mentions that, “In this book there are listings of trigonometric tables for the ‘Sind’ and the ‘Hind’, better known as ‘Sinus’ and ‘Cosinus’ which now form the basis of almost all trigonometric formulas”. Here, Jafoufi was referring to Al-Khwarizmi’s book ‘Zij al-Sindhind’ and how work shown there displayed Al-Khwarizmi’s knowledge in trigonometry and how he used it to complete trigonometric astronomical tables. This allowed him to interpret the movement of celestial bodies. Al-Khwarizmi was able to provide very accurate tables for the trigonometric functions of sine and cosine in his time. This meant that Al-Khwarizmi was able to calculate the sine and cosine values for special angles such as 0°, 30°, 45°, 60° and 90°. Later on, he was also able to create tangent tables,