Euclid biography pdf. C and taught in Alexandria Egypt.

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Leonard Mlodinow's Euclid’s Window provides a narrative on the evolution Euclid biography - Copy(1). 300 B. But if you don’t know how to download and install PD Are you tired of struggling to download PDF files from Google? Look no further. Most sources estimate h Euclid was a Greek mathematician who developed a theorem that was later named in his honor as the Euclidean Algorithm. O In today’s digital age, PDFs have become an indispensable tool for sharing and preserving information. It includes details about his life and major work Elements, which is considered one of the most influential works in the history of mathematics. This beginner-friendly PDF guide is here to help you master the basics of coding. Euclid's most famous work is his collection of 13 books, dealing with geometry, called The Elements. His life and legacy continue to inspire millions of peopl Solomon Saprid was a Philippine artist known for his bronze sculptures that involved welding scraps of metal together, making the piece look jagged. He wrote them at about 300 BC. It was he who shaped geometry into what it is today. " Sep 16, 2017 · Although Euclid is a famous mathematician, very little is known about his life. With the wide range of options available, it can be overwhelming to choose the righ Have you ever encountered the frustrating situation where you try to open a PDF file, but it simply won’t open? Whether it’s an important document or an ebook you’ve been eager to In today’s digital world, PDF files have become an essential format for sharing and preserving documents. He grew up on a ranch and has been involved in ranching for many years. Euclid obtained his education at Plato’s Academy in Athens, Greece and then moved to Alexandria. Are you tired of searching for the perfect PDF program that fits your needs? Look no further. , ‘every positive integer greater than 1 can be written as a prime number or is itself a prime number’. Includes editions and translations of Euclid's Elements, Data, and Optica, Proclus's Commentary on Euclid, and other historical sources. Whether you need to create an e-book, share a presentation, or simply conv PDF, or Portable Document Format, is a popular file format used for creating and sharing documents. Renowned for his expertise in ancient military history, classical literature, and contemp Freddie Mercury, born Farrokh Bulsara, was a legendary British musician and the lead vocalist of the iconic rock band Queen. He captivated audiences worldwide with his powerful voi Paul, who was originally called “Saul of Tarsus”, was one of the most important leaders of the “Apostolic Age” in the first century A. 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Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. ಅವರು ಒಂದನೇ Euclid (c. A two page biography of Greek Mathematician, Euclid, known as the Father of Geometry. It is believed that he was a student of Plato. ) by Heinz Klaus Strick, Germany The pictured postage stamp from Sierra Leone shows a Euclid biography by Charlene Douglass With extensive bibliography. 5 pages at 300 words per page) View a FREE sample. All sources on the life of Euclid agree on two points. Login. 530 ce). The title led me to believe this book may contain factual or misleading information. 305-285 BC). She was previously known as the second and last wife of Doctor Gene Scot Leslie Sansone was born in New Castle, Pennsylvania, on Feb. A reckoning is a measuring of possibilities for the future. Biography: Euclid, Father of Geometry Overview This Biography: Euclid, Father of Geometry is perfect to practice geometry skills. (1989). So Euclid grew up in a city that was becoming the most important in the world. A clear exposition of the "errors" of Euclid and of the solutions presented in the Grundlagen der Geometrie, with reference to non-Euclidean geometry. Secondly, in spite of this, very little is known about his life. These biographies contain personal and professional information If you are a registered nurse writing a personal biography, then consider who your audience is and include information about credentials and your current situation, including the r Writing your own biography can be an exciting and rewarding experience. However, there are times when you may need to extract specific pages from a P Are you interested in learning how to code but don’t know where to start? Look no further. The Ptolemaic Era (i. Jul 24, 2016 · Note: अगर आपके पास Euclid Biography in Hindi मैं और Information हैं। या दी गयी जानकारी मैं कुछ गलत लगे तो तुरंत हमें कमेंट मैं लिखे हम इस अपडेट करते रहेंगे। In the Middle Ages, writers sometimes referred to him as Euclid of Megara, confusing him with a Greek Socratic philosopher who lived approximately one century earlier. It is said that Euclid established a mathematical school in Alexandria. Little is known about Euclid’s life. Some scholars have argued that Euclid biography by Charlene Douglass With extensive bibliography. pdf), Text File (. His textbook ‘Elements’ remained a highly influential mathematics teaching book until the late 19th Century and is one of the most widely published books in the world. 25 Possible copyright status NOT_IN_COPYRIGHT Ppi 600 Scandate 20070613000000 Euclid - Free download as Word Doc (. In 1980, 18-year-old Leslie took a weekend certification course to become an aerobic instructor to help pay f The book “Marky Mark” by Mark Wahlberg and Lynn Goldsmith includes interviews with Wahlberg, his brother Donnie Wahlberg and other members of his family. As a result, he became known as the father of geometry. See full list on britannica. 1 / 8 EUCLID OF ALEXANDRIA (ca. Whether you are a professional looking to enhance your online presence In the digital age, a compelling biography can make all the difference in capturing the attention of your audience. Behind every great musician lies a fascinating story of struggle, determination, and triumph. Nov 2, 2017 · Euclid is an author who took the ideas and inventions of others and combined them all into a series a books in which he attempted to prove the existing ideas. New York: Dover Publications. ಯೂಕ್ಲಿಡ್‍ರವರು ಅಲೆಕ್ಸಾಂಡ್ರಿಯದಲ್ಲಿ ಹುಟ್ಟಿದರು. txt) or read online for free. %PDF-1. At the time, Alexandria was a young city. The document summarizes the biographies and major mathematical contributions of 28 famous mathematicians from history. Although little is known about Euclid the man, he taught in a school that he founded in Alexandria, Egypt, around 300 b. pdf) or read online for free. Většinu života strávil v Alexandrii v Egyptě. Euclid biography. Hilbert. 14, 1962. Euclid Resources Euclid has remained one of the founding mathematicians. Euclid biography facts; Euclid biography facts and information; Euclid short biography; Euclid biography pdf; Euclid born and died date; Due to this reason, the world knows him as the father of geometry. Although it was initially thought that he was born in Megara, a Greek city, it was later revealed that Euclid of Megara was a philosopher who lived a century before Euclid of Alexandria, the author of E Euclid of Alexandria was a Greek geometer whose floruit was c. Euclid’s Postulate 4: That all right angles are equal to one another. 325 BC – 265 BC) – Greek Mathematician considered the “Father of Geometry”. Greco-Roman era) had just began, considering the fact that Alexander the Great’s most trusted companion general Ptolemy I Soter was ruler of Egypt (r. Euclid founded his own school in Alexandria, Egypt, and gained a reputation as an exceptional geometry teacher. (1) Hence, this biography of Euclid considers the scant information about his life Euclid Biography & Father Of Geometry or Euclid Information in Marathi Language - भूमितीचा जन्मदाता महान युक्लीड यांचे जिवनचरित्र Euclid biography pdf Rating: 4. 33(2), 381-393, (Summer 2003) Euclid of Alexandria was an ancient Greek mathematician, who is regarded as the ‘father of geometry’. ISBN 0-486-60088-2. His name is also present in the modern geometry book as “Euclidean geometry”. He also made seminal contributions in analytic geometry, complex Euclid (abad ke-4 SM) adalah matematikawan dari Alexandria, Mesir yang dianggap sebagai bapak geometri. According to Proclus (410-485 A. to reject the assessment of Euclid's character . BIOGRAPHY OF MATHEMATICIANS - Free download as Word Doc (. Jones, Ellen E. Help | Contact Us Thomas Bayes, from whom Bayes theorem takes its name, was probably born in 1701, so the year 2001 marked the 300th anniversary of his birth. ) he said that Euclid came after the first pupils of Plato and lived during the reign of Ptomlemy I (306-283 B. A biography is typically writte Writing your own biography in third person means one is writing about oneself as if someone else were telling the story, using the pronouns “he” or “she” instead of “I. 4 3 0 obj /Length 457 /Filter /FlateDecode >> stream xÚu’ÍnÛ0 „ï~ % Újù³ rD[ I è IÚC 8h 6=ôíK‘² Ή rø-g–k·ú¼a > Oct 23, 2015 · The philosopher Proclus of Athens (412-485 CE), who lived seven centuries later, said that Euclid "put together the Elements, collecting many of Eudoxus's theorems, perfecting many of Theaetetus's, and bringing to irrefragable demonstration things which were only somewhat loosely proved by his predecessors. Feb 20, 2022 · The earliest biography of Plato to date, De Platone et dogmate eius, is by a second-century Latin author, Apuleius. Some scholars have argued that He wrote them at about 300 BC. He wrote Elements, the most influential mathematics work of all time, which served as the primary mathematics textbook from its publication until the late 19th century. Although little is known about his early and personal life, he went on to contribute greatly in the field of mathematics and came to known as the ‘Father of Geometry’, Euclid is known to have taught mathematics in Ancient Egypt during the reign of Ptolemy I. She was married to Saint Felix, with whom she died. Find out the controversies and uncertainties surrounding his identity, dating and authorship. In the history of mathematics, one of the highly esteemed work of all time was his Elements. This biography was written to celebrate this anniversary. Euclid was an important Greek mathematician who lived in Alexandria around 300 BC His most famous work was The Elements, a 13-volume treatise on geometry and number theory that was used as a standard text for more than 2,000 years. He was born in 330 B. It provides a universal platform for sharing information across different device The reason for a PDF file not to open on a computer can either be a problem with the PDF file itself, an issue with password protection or non-compliance with industry standards. 300 BC) was an ancient Greek mathematician active as a geometer and logician. All of Plato's other biographies were written more than five hundred years after Since there are very few historical references to the Greek mathematician Euclid’s life, the circumstances and even the exact year of his death are unknown. Includes editions and translations of Euclid's Elements , Data , and Optica , Proclus's Commentary on Euclid , and other historical sources. Euclid was a Greek mathematician from Alexandria who lived around 300 BC. . Thron," Rocky Mountain Journal of Mathematics, Rocky Mountain J. These stories are o A personal biography is a powerful tool that allows you to showcase your achievements, experiences, and personality in a concise and engaging way. Greek mathematician Euclid was born in the latter part of the 4 th century BC (most likely around 320 BC) in the City of Alexandria in Egypt. It Nov 9, 2021 · Access-restricted-item true Addeddate 2021-11-09 08:06:52 Associated-names Heath, Thomas Little, Sir, 1861-1940 Boxid Euclid’s ‘The Elements’ Euclid’s ‘Elements’ contains 465 propositions, 93 problems and 372 theorems in thirteen volumes. e. He invented the form of mathematical proof that is still used today. 300 bc, Alexandria, Egypt), Greek mathematician of antiquity, known primarily for his highly influential treatise on geometry, the Elements. with full statements Since 2007, the English Wikipedia page of Euclid has received more than 6,428,265 page views. PDF Cite Share Euclid, a Greek mathematician, laid the foundation of geometry as we understand it today. C. The Thirteen Books of Euclid's Elements, Vol. – asi 260 př. The document discusses the history of early mathematics from ancient cultures including Egypt, Mesopotamia, India, China, and Greece. 300 bce. Saprid was born on March 13, 19 Victor Davis Hanson is a name that resonates within the academic and intellectual circles. Euclid’s Postulate 3: To describe a circle with any center and distance. Learn about the life and works of Euclid, the Greek mathematician who wrote The Elements, the most influential treatise on geometry. Reid, Constance. He is often referred to as the "Father of Geometry" and is best known for his influential textbook Elements, which was one of the most widely used mathematics Jul 28, 2012 · Euclid was a Greek mathematician from Alexandria, Egypt in the 3rd century BC. The document provides biographical information about the Greek mathematician Euclid. Euclid is the 5th most popular mathematician (up from 8th in 2019), the 4th most popular biography from Egypt (up from 7th in 2019) and the most popular Egyptian Sign In View Cart Help Euclid_Elements_Book I_Proposition 1 - Free download as PDF File (. Euclid founded his own school in Alexandria, Egypt, and gained a reputation as an exceptional geometry teacher Euclid of Alexandria (lived cBCE) systematized ancient Greek and Near Eastern mathematics and geometry. Pythagoras was a Greek philosopher, scientist and religious scholar born in the 6th century BCE. Are you looking to write a captivating biography but don’t know where to start? Writing a biography can be a daunting task, but with the right approach and some real-life examples, Elements of a biography include the person’s date of birth, major accomplishments, career summary and an overview of why the person is interesting or important. De Interpretatione: Commented Biography of Euclid - Volume 48 Issue 192 However, as you have access to this content, a full PDF is available via the ‘Save PDF © Heinz Klaus Strick Leverkusen, p. Rowe, D. PDF - Google Drive Sign in Euclid biography pdf Rating: 4. Euclid lived long ago in Alexandria, Egypt. Euclid has remained one of the founding mathematicians. Further, Euclid was greatly criticized because his assumptions were far too liberal. com within the “TMZ on TV” entry. In this article, we will guide you through the process of downloading and installing a To find out more information about the Secrets in Lace models, visit their blog on the official Secrets in Lace models website. Pythagoras was a student of a Euclid b Thales c Archimedes d Bhaskara. [2] Considered the "father of geometry", [3] he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. Consists of 36 propositions concerning the division of various figures into two or more equal parts or parts in given ratios. He founded a school in Croton, Italy where he taught mathematics and religious concepts. It was presumably at Alexandria, according to a story by Stobaeus, 17 that someone who had begun to learn geometry with Euclid asked him, after the first theo-rem, what he got out of such things . , and he was the son of Naucratis. Reference Heath, Thomas L. Jan 17, 2025 · Euclid - Geometry, Elements, Mathematics: In ancient times, commentaries were written by Heron of Alexandria (flourished 62 ce), Pappus of Alexandria (flourished c. Euclid biography pdf A robust timeline chronically the dozens of event in the life of the 16th president Abraham Lincoln. ISBN 0-387-94674-8. It has had a lasting influence on the sciences -, especially in mathematics. Reed, Fred W. Euclid’s Postulate 5: That, if a straight line falling on two straight lines make the PDF రూపంలో దించుకోండి Euclid) (గ్రీకు MacTutor Biography Archived 2011-06-07 at the Wayback Machine; Euclid's Euclid biography by Charlene Douglass With extensive bibliography. Whether you are an individual seeking to create a personal brand A biography is a powerful tool that allows us to delve into the lives of remarkable individuals, gaining insight into their achievements, experiences, and contributions. He is famous as the father of geometry, as his influential Elements of Geometry has been read, edited, praised, or criticized more than any other mathematical book in history. Most history states that he was a kind, fair, patient man. Biography of Euclid - Free download as Word Doc (. Source for information on Euclid and His Contributions: Mathematics dictionary. Contact & Support. Euclid was a Greek mathematician from Alexandria who lived in the late 4th century BC. His work appeared during the time of Ptolemy I. Summoning a slave, Euclid said, "Give him three obols, since he must needs make gain out of what he November 27, 2004, marked the 250th anniversary of the death of Abraham De Moivre, best known in statistical circles for his famous large-sample approximation to the binomial distribution, whose generalization is now referred to as the Central Limit Theorem. Mathematicians usually refer to him simply as "Euclid," but he's sometimes called Euclid of Alexandria to avoid confusion with the Green Socratic philosopher Euclid of Megara. He was a pupi l of S ocrates and Euclid of Alexandria was a Greek mathematician who lived from around 325 BC to 265 BC. E. May 19, 2009 · The thirteen books of Euclid's Elements Pdf_module_version 0. doc / . De Moivre was one of the great pioneers of classical probability theory. Your personal biography should be In today’s digital age, personal biographies have become an essential tool for individuals in various fields. Biography. With so many options available, it can be overwhelming to choose t Are you looking for a simple and cost-effective way to merge your PDF files? Look no further. His biography is available in 157 different languages on Wikipedia (up from 150 in 2019). Euclid was born in 325 BCE in No other source records Euclid’s homeland, though ignorance of this has naturally encouraged speculation, including the wild hypothesis that ‘Euclid’ was the pseudonym of an ancient mathematical collective à la ‘Nicolas Bourbaki’, rather than an historical individual. He is considered the "Father of Geometry" and is best known for his influential textbook Elements, which laid out the principles of geometry and became the main textbook for teaching mathematics for over 2000 years. ). The biography can cover the subject’s entire life or a distinct portion. I Are you tired of dealing with paper forms that are time-consuming to fill out and prone to errors? Creating fillable PDF forms can be a game-changer for your business or organizati In today’s digital world, the ability to convert files from one format to another is crucial. But there is some speculation about if this man really existed. Euclid's Elements is a famous Greek mathematical text composed around 300 BC. Euclid’s Optics was an immensely influential book on light and vision. Euclid of Megara : is a p hilosopher who l i ved about 100 years bef ore t he mathematician Eucl i d of Al exandria. This section contains 1,261 words (approx. He is known as the "Father of Geometry" for his influential textbook The Elements, which was used as the standard geometry textbook for over 2000 years. He is considered the "Father of Geometry" and is best known for his influential textbook "Elements", which was one of the most widely published books Nov 21, 2023 · Euclid was a Greek mathematician who lived in the city of Alexandria around 300 BC. The introd Les Feldick was born on June 6 of 1927, in Kinta, Oklahoma. n. ” Short biog Those interested in learning more about Jill Swaggart can read her biography on her LinkedIn. Firstly, he was the most prominent mathematician of antiquity, best known for his work The Elements, which has been read and reread for generations making him the leading mathematics teacher of all time. Math. Euclid was a renowned Greek mathematician from ancient Egypt known as the "Father of Geometry". tlm4all@Euclid biography. Jones," Rocky Mountain Journal of Mathematics, Rocky Mountain J. Jun 24, 2018 · Kyle Gabriele MAT - 301 3-17-18 Euclid biography Euclid, known as Eukleides was known as the father of Geometry and changed the course of the world. Business Office 905 W. Many times, we come across PDF files that we want to share or use in different ways. in Alexandria, Egypt and lived until about 300 B. Mar 2, 2019 · Euclid of Alexandria lived in 365-300 BC (approximately). (MLK) is widely regarded as one of the most influential figures in American history. Euclid explained light’s behavior using geometrical principles he had developed in the Elements. 1 (2nd ed. Alexander the Great had conquered ancient Egypt and founded Alexandria in about 332 bce. JSTOR is a digital library of academic journals, books, and primary sources. D. Study Materials. Is anything known about Euclid's family? Almost nothing is known about Euclid's life. 21 The Thirteen Books of Euclid's Elements, Premium PDF. He continued studying mathematics, physics, Are you looking for free PDFs to use for your business or personal projects? If so, you’ve come to the right place. Texts on Ancient Mathematics and Mathematical Astronomy PDF scans (Note: many are very large files). It served as a prescribed textbook for teaching mathematics from its publication till … Euclid - The Creation of Mathematics "The author invites the ‘lover of mathematics’ to have a peek, via a gentle introduction and presentation of Euclid’s Elements, with detours to previous Greek geometers, whose work has been incorporated in the Elements. E. The current sketch of his life includes his family background and education, as well as his scientific and theological work. ” This is a name that looms large in the history of mathematics and throughout the field of science. Your elementary grade students will love this Biography: Euclid, Father of Geometry. Main Street Suite 18B Durham, NC 27701 USA. The Elements is one of the most influential books ever written. Her brand also offers home Saint Lillian is a pre-congregational saint who lived and was martyred in Cordova, Spain in the mid-ninth century. In this article, we will share expert tips on how to merge PDF files for free, saving PDFs are a great way to share documents, forms, and other files. Euclid was born around 365 B. com Jan 1, 2022 · Euclid, a Greek mathematician, flourished around 300 BCE. To begi. His theory of light was the basis of artistic perspective, astronomical methods, and navigation methods for more than two thousand years. Thomas Bayes, from whom Bayes theorem takes its name, was probably born in 1701, so the year 2001 marked the 300th anniversary of his birth. Some authors claim that he was born and lived in Alexandria, northern Egypt during the reign of Ptolemy I, while others claim that his birth was in Tyre Kingdom and that he lived in Damascus. l. It set a standard for deductive reasoning and geometric instruction that persisted, practically unchanged, for more than Euclid Mathematician Specialty Euclidean geometry Nationality Greek Euclid, an ancient Greek mathematician, is often referred to as “the Father of Geometry. The text covers topics in plane and solid geometry, number theory, and incommensurable lines. c. NCERT Solutions. 3 The epithet ‘Alexandrinus’ is modern and stems from confusion May 16, 2024 · Euclid was a great Greek mathematician. Euclid (/ ˈ j uː k l ɪ d /; Ancient Greek: Εὐκλείδης; fl. Paul Cox wanted “a biography put together of the Greek mathematician, Euclid. He developed a version of the fundamental theorem of arithmet A biography must cover the accounts of a person’s life in the third-person. Due to this reason, the world knows him as the father of geometry. An account is to furnish a reckoning. Biography – Life Span Euclid was born in 325 BCE Elements, treatise on geometry and mathematics written by the Greek mathematician Euclid (flourished 300 bce). Download the entire Euclid study guide as a printable PDF! Elizabeth George Speare Biography; Biography of Mathematicians - Free download as Word Doc (. It is considered one of the most influential works in the development of logic and science. The mathematicians spanned different eras and nationalities and made breakthroughs Jun 24, 2018 · Kyle Gabriele MAT - 301 3-17-18 Euclid biography Euclid, known as Eukleides was known as the father of Geometry and changed the course of the world. Though he dedicated the early part of his l Euclid discovered the concept underlying the exponent, calling the area of a square a power of the length of a single side. pdf - Free download as PDF File (. Euclid gave the proof of a fundamental theorem of arithmetic, i. Some of the mathematicians featured include Albert Einstein, Isaac Newton, Leonardo Fibonacci, Pythagoras, Euclid, Archimedes, Ada Lovelace, Alan Turing, Srinivasa Ramanujan, and Emmy Noether. In contrast to some, but not all, biographies of Bayes, the current Subscribe to Project Euclid Receive erratum alerts for this article William B. 0. The Elements compiled the knowledge of previous mathematicians into 13 volumes covering topics like triangles, circles, proportions, and solid geometry. NCERT Solutions For Class 12. 335–405 ce), edited the Elements with textual changes and some additions; his version quickly drove other editions यूक्लिड का जीवन परिचय। Euclid ka Jivan Parichay : यूक्लिड (Euclid) ग्रीक गणितज्ञ थे, जो ईसा से लगभग ३२५ वर्ष पूर्व हुए थे। यूक्लिड ने एलिमेण्ट्स (Elements) नामक एक पुस्तक लिखी जो 13 Euclid’s Postulate 2: To producea finite straight line continuously in a straight line. Whether it’s for personal or professional use, PDFs are a versatile and convenient file format. The Moors, an Martin Luther King Jr. The length of the b Many staff biographies, such as for TMZ editor Harvey Levin, are available at IMDb. Archimedes later generalized the idea of powers in his w The inventor of geometry was Euclid, and his nickname was The Father of Geometry. Kontribusinya yang paling berpengaruh adalah buku The Elements yang menjadi dasar pengajaran geometri hingga saat ini dengan mendefinisikan konsep-konsep seperti titik, garis, dan sudut serta memberikan aksioma-aksioma untuk membuktikan teorema-teorema geometri. Biography – Life Span Euclid was born in BCE. He is best known for his work with geometry. This guide will provide you with all the information you need to Have you ever encountered the frustration of trying to open a PDF file on your device only to find that it refuses to cooperate? You’re not alone. The contents of the Elements are presented book by book . His most renowned work is " Elements ” and is composed of thirteen books that develop different geometric and arithmetic themes, and that have remained unchanged Sep 22, 2021 · Biography. ” A biography is an account of a person’s life described by another. However, pu When it comes to handling and viewing PDF files, having the right software installed on your computer is crucial. doc), PDF File (. They are easy to use, secure, and can be opened on any device. The biography, which was f Subhash Chandra Bose, also known as Netaji, was a prominent figure in India’s struggle for independence from British rule. org. Subscribe to Project Euclid Receive erratum alerts for this article Phil Gustafson "Biography of William B. Pengaruh pemikiran Euclid Euclid of Alexandria : i s t he most prominent m athematician of ant i qui t y best known for his tre at i se on mat hemat i cs T he Elements. The blog provides photos and biographies of several Archimedes went to school at the Royal Library of Alexandria in Egypt under the guidance of former students of the mathematician Euclid. Euclid and His Contributions Euclid was an ancient Greek mathematician from Alexandria who is best known for his major work, Elements. (1996). It allows you to reflect on your life journey, accomplishments, and the lessons you’ve learned along the way Whether you’re an aspiring writer, a professional looking to enhance your online presence, or simply someone interested in documenting their life story, writing your own biography A biography is the story of a person’s life in the words of another person, while an autobiography is the story of a person’s life in his own words. He contributed many things to geometry due to his keen interest. 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