Final answer:
The terms 'algebra' and 'algorithm' originated from the Arabic mathematician al-Khwarizmi. 'Algebra' comes from his influential book on the subject, while 'algorithm' is derived from his name. Other terms like 'decimal', 'fraction', 'perfect square', 'remainder', and 'root' are concepts developed later with Arabic scholars contributing significantly.
Step-by-step explanation:
Mathematical Terms Originated from al-Khwarizmi
Among the terms that originated from the work of the Arabic mathematician, al-Khwarizmi, are algebra and algorithm. The term algebra comes from his seminal book 'ilm al-jabr wa'l-muqabala, which translates to "the science of restoring what is missing and equating like with like." This treatise laid the foundation for Algebra as we know it today. The term algorithm derives from al-Khwarizmi, his name being Latinized in the transliteration process. Although al-Khwarizmi's work was influential in the development of the decimal system and his texts often discussed fractions and roots, the terminology for decimal, fraction, perfect square, remainder, and root does not directly originate from his name or specific works but are rather concepts that were later expanded upon, with Arabic scholars playing a significant role in their development.
Arabic mathematicians were greatly influenced by Indian mathematics, which had already introduced decimals, the concept of zero, and had made strides in trigonometry. The synthesis of knowledge across different cultures, including Arabic, Persian and Indian contributions, allowed for the progression of mathematics, which in turn supported major scientific breakthroughs during the Scientific Revolution and beyond.