Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja
Encyclopedia
Jagadguru Swami Sri Bhārati Kṛṣṇa Tīrthaji Mahāraja (Sanskrit: जगद्गुरु स्वामि श्री भारती कृष्ण तीर्थजी महाराज; March, 1884 – February 2, 1960) was the Jagadguru
Jagadguru
Jagadguru , literally meaning the Guru of the world, is a title used in Sanatana Dharma. Traditionally, it has been bestowed upon or used for acharyas belonging to the Vedānta school who have written Sanskrit commentaries on the Prasthānatrayī - the Brahma Sutra Jagadguru (Sanskrit जगद्गुरु),...

 (literally, teacher of the world; assigned to heads of Hindu mathas
Matha
A matha ) is a term for monastic and similar religious establishments of Hinduism and Jainism. A matha is usually more formal, hierarchical, and rule-based than an ashram.-Advaita Mathas:...

) of the Govardhana matha
Govardhana matha
The Govardhana matha is located in the city of Puri in Orissa state , and is associated with the Jagannath temple. It is one of those four cardinal mathas said to have been founded by Adi Shankara, and is the eastern matha. As per the tradition initiated by Adi Shankara, it is in charge of the Rig...

 of Puri
Puri
Puri is district headquarter, a city situated about south of state capital Bhubaneswar, on the eastern coast of the Bay of Bengal in the Indian state of Orissa. It is also known as Jagannath Puri after the Jagannath Temple . It is a holy city of the Hindus as a part of the Char Dham pilgrimages...

 during 1925–1960. He was one of the most significant spiritual figures in Hinduism
Hinduism
Hinduism is the predominant and indigenous religious tradition of the Indian Subcontinent. Hinduism is known to its followers as , amongst many other expressions...

 during the 20th century. He is particularly known for his book Vedic Mathematics
Vedic Mathematics (book)
The book Vedic Mathematics was written by Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja. It describes his Vedic mathematics, a system of mental calculation. Bharati claimed he had found the basis of this system written in the form of sutras in an appendix of Atharvaveda which has now been...

.

Early life

Venkatraman Shastri was born in March, 1884 to P. Narasimha Shastri, originally a tehsildar at Tirunelveli
Tirunelveli
Tirunelveli , also known as Nellai , and historically as Tinnevelly, is a city in the Indian state of Tamil Nadu. It is the headquarters of the Tirunelveli District and the sixth biggest city in Tamil Nadu...

 in Madras Presidency
Madras Presidency
The Madras Presidency , officially the Presidency of Fort St. George and also known as Madras Province, was an administrative subdivision of British India...

. Narasimha Shastri later became the Deputy Collector of the Presidency. Venkatraman was born in a highly illustrious family. His uncle, Chandrasekhara Shastri was the Principal of the Maharaja's College in Vizianagaram
Vizianagaram
Vizianagaram is the main city of the Vizianagaram District of north-eastern Andhra Pradesh in southern India. Vizianagaram district was formed on 1 June 1979, with some parts carved from the neighbouring districts of Srikakulam and Visakhapatnam. It is, at present, the largest municipality of...

, while his great-grandfather, Justice C. Ranganath Shastri was a judge
Judge
A judge is a person who presides over court proceedings, either alone or as part of a panel of judges. The powers, functions, method of appointment, discipline, and training of judges vary widely across different jurisdictions. The judge is supposed to conduct the trial impartially and in an open...

 in the Madras High Court
Madras High Court
The Madras High Court is a senior court located at Chennai , in India. The court buildings, which are believed to be the second largest judicial complex in the world, are located near the beach, in one of the city's major business districts....

.

Educational career

Venkatraman Shastri started his educational career as a student of the National College in Trichanapalli. After that he moved to the Church Missionary Society College and eventually the Hindu College, both in Tirunelveli
Tirunelveli
Tirunelveli , also known as Nellai , and historically as Tinnevelly, is a city in the Indian state of Tamil Nadu. It is the headquarters of the Tirunelveli District and the sixth biggest city in Tamil Nadu...

. He was consistently held first place in all subjects in all of his classes. Shastri passed his matriculation
Matriculation
Matriculation, in the broadest sense, means to be registered or added to a list, from the Latin matricula – little list. In Scottish heraldry, for instance, a matriculation is a registration of armorial bearings...

 examination from the Madras University in January, 1899, where he also finished at the head of the class.

As a student Venkatraman was marked for his splendid brilliance, superb retentive memory and an insatiable curiosity. By deluging his teachers with piercing questions, making them uneasy, and frequently forcing them to admit ignorance he was considered a terribly mischievous student.

Although Venkatraman always scored high in subjects like mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, sciences and humanities
Humanities
The humanities are academic disciplines that study the human condition, using methods that are primarily analytical, critical, or speculative, as distinguished from the mainly empirical approaches of the natural sciences....

, he was also proficient in languages and particularly adept in Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...

. According to his own testimonials, Sanskrit and oratory
Oratory
Oratory is a type of public speaking.Oratory may also refer to:* Oratory , a power metal band* Oratory , a place of worship* a religious order such as** Oratory of Saint Philip Neri ** Oratory of Jesus...

 were his favourite subjects. Such was his mastery over the language, that he was awarded the title "Saraswati" by the Madras Sanskrit Association in July, 1899 at the age of 16. At about that time, Venkatraman was profoundly influenced by his Sanskrit guru
Guru
A guru is one who is regarded as having great knowledge, wisdom, and authority in a certain area, and who uses it to guide others . Other forms of manifestation of this principle can include parents, school teachers, non-human objects and even one's own intellectual discipline, if the...

 Sri Vedam Venkatrai Shastri whom he remembered with deepest love, reverence and gratitude, with tears in his eyes.

Venkatraman won the highest place in the graduation B.A.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...

 examination in 1902. He then appeared for the M.A.
Master's degree
A master's is an academic degree granted to individuals who have undergone study demonstrating a mastery or high-order overview of a specific field of study or area of professional practice...

 Examination for the American College of Sciences, in Rochester, New York
Rochester, New York
Rochester is a city in Monroe County, New York, south of Lake Ontario in the United States. Known as The World's Image Centre, it was also once known as The Flour City, and more recently as The Flower City...

 from the Bombay centre in 1903. He passed the M.A. examination in seven subjects that he had chosen - Sanskrit, philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

, English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

, mathematics, history
History
History is the discovery, collection, organization, and presentation of information about past events. History can also mean the period of time after writing was invented. Scholars who write about history are called historians...

, science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

 and another - simultaneously scoring the highest honours in all, which was perhaps an all-time world record
World record
A world record is usually the best global performance ever recorded and verified in a specific skill or sport. The book Guinness World Records collates and publishes notable records of all types, from first and best to worst human achievements, to extremes in the natural world and beyond...

 at the time.

Venkatraman Saraswati, as he was called after receiving the title, also contributed to W. T. Stead's Review of Reviews
Review of Reviews
The Review of Reviews was a noted family of monthly journals founded in 1890-93 by British reform journalist William Thomas Stead...

on topics as diverse as religion and science. During his college days, he also wrote extensively on history, sociology
Sociology
Sociology is the study of society. It is a social science—a term with which it is sometimes synonymous—which uses various methods of empirical investigation and critical analysis to develop a body of knowledge about human social activity...

, philosophy, politics
Politics
Politics is a process by which groups of people make collective decisions. The term is generally applied to the art or science of running governmental or state affairs, including behavior within civil governments, but also applies to institutions, fields, and special interest groups such as the...

 and literature
Literature
Literature is the art of written works, and is not bound to published sources...

. Reading of the latest scientific research and discoveries was his hobby throughout his life.

Early public life

Venkatraman Saraswati worked under Gopal Krishna Gokhale
Gopal Krishna Gokhale
Gopal Krishna Gokhale, CIE was one of the founding social and political leaders during the Indian Independence Movement against the British Empire in India. Gokhale was a senior leader of the Indian National Congress and founder of the Servants of India Society...

 in 1905 for the National Education Movement and the South African Indian problems. However, his inclination towards science and Hindu studies
Hindu studies
Hindu studies is the study of the traditions and practices of the Indian subcontinent, especially Hinduism. Beginning with British philology in the colonial period, Hindu studies has been practiced largely by Westerners, due in part to the lack of a distinct department for religion in Indian academia...

 led him to study the ancient Indian
History of India
The history of India begins with evidence of human activity of Homo sapiens as long as 75,000 years ago, or with earlier hominids including Homo erectus from about 500,000 years ago. The Indus Valley Civilization, which spread and flourished in the northwestern part of the Indian subcontinent from...

 holy scriptures, Adhyātma-Vidyā. In 1908 he joined the Sringeri Matha in Mysore to study under the Sringeri Shankaracharya
Shankaracharya
Shankaracharya, is a commonly used title of heads of mathas in the Advaita Vedanta tradition. The title derives from Adi Shankara, a 9th century CE reformer of Hinduism. He is honored as Jagadguru, a title that was used earlier only to Lord Krishna...

 Sri Satchidānanda Sivābhinava Nrisimha Bhārati Swami. However, his spiritual practise was interrupted when he was pressurized by nationalist leaders to head the newly started National College at Rajamahendri. Prof. Venkatraman Saraswati taught at the college for three years. But in 1911, he suddenly left the college to go back to Sri Satchidānanda Sivābhinava Nrisimha Bhārati Swami at the Sringeri Math in his quest for spiritual knowledge.

Spiritual path

Returning to Sringeri, Venkatraman spent his next eight years studying advanced Vedanta
Vedanta
Vedānta was originally a word used in Hindu philosophy as a synonym for that part of the Veda texts known also as the Upanishads. The name is a morphophonological form of Veda-anta = "Veda-end" = "the appendix to the Vedic hymns." It is also speculated that "Vedānta" means "the purpose or goal...

 philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

 at the feet of Shri Nrisimha Bhārati Swami.

He also practised vigorous meditation, Brahma-sadhana and Yoga-sādhāna
Yoga
Yoga is a physical, mental, and spiritual discipline, originating in ancient India. The goal of yoga, or of the person practicing yoga, is the attainment of a state of perfect spiritual insight and tranquility while meditating on Supersoul...

during those years in the nearby forests. It is believed that he attained spiritual
Spirituality
Spirituality can refer to an ultimate or an alleged immaterial reality; an inner path enabling a person to discover the essence of his/her being; or the “deepest values and meanings by which people live.” Spiritual practices, including meditation, prayer and contemplation, are intended to develop...

 self-realization during his years in the Sringeri Math. He would leave the material world and practise Yoga meditation in seclusion for many days. During those eight years, he also taught Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...

 and Philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...

 to local schools and ashrams. He delivered a series of sixteen lectures on Shankaracharya's philosophy at Shankar Institute of Philosophy, Amalner [Khandesh]. During that time, he also lectured as a guest professor at various institutions in Mumbai
Mumbai
Mumbai , formerly known as Bombay in English, is the capital of the Indian state of Maharashtra. It is the most populous city in India, and the fourth most populous city in the world, with a total metropolitan area population of approximately 20.5 million...

, Pune
Pune
Pune , is the eighth largest metropolis in India, the second largest in the state of Maharashtra after Mumbai, and the largest city in the Western Ghats. Once the centre of power of the Maratha Empire, it is situated 560 metres above sea level on the Deccan plateau at the confluence of the Mula ...

 and Khandesh
Khandesh
Khandesh is a region of central India, which forms the northwestern portion of Maharashtra state.Khandesh was the terminal territorial part under the rule of Mughals. The Start of Deccan region demarcated by the boundary of Khandesh....

.

Initiation into Sanyasa order

After Venkatraman's eight-year period of spiritual practice and study of the Vedanta and Vedic philosophy, he was initiated into the holy order of Samnyasa at Benaras by Jagadguru Shankaracharya Sri Trivikram Tirthaji Maharaj of Shāradāpeeth on July 4, 1919 and on this occasion he was given the title of Swami
Swami
A swami sometimes abbreviated "Sw." is an ascetic or yogi who has been initiated into the religious monastic order founded by Adi Sankara, or to a religious teacher.The Oxford English Dictionary gives the etymology as...

and the new name, "Swami Bhārāti Kṛṣṇa Tīrtha".

Shankaracharya of Sharada Peetha

Swami Bhārāti Kṛṣṇa Tīrtha was installed as Shankaracharya
Shankaracharya
Shankaracharya, is a commonly used title of heads of mathas in the Advaita Vedanta tradition. The title derives from Adi Shankara, a 9th century CE reformer of Hinduism. He is honored as Jagadguru, a title that was used earlier only to Lord Krishna...

 of Sharada Peetha
Sringeri Sharada Peetham
Sringeri Sharada Peetham is the southern Advaita Vedanta matha. It is located in Shringeri. It is claimed that it is the first of the four original mathas established by Adi Shankara.-Location:...

 in 1921 after just two years of Sanyasa. After assuming the pontificate Shri
Jagadguruji, he was given another title, Jagadguru, as is the tradition. The Swami then toured India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...

 from corner to corner giving lectures on Sanātana Dharma, Vedic philosophy and Vedanta
Vedanta
Vedānta was originally a word used in Hindu philosophy as a synonym for that part of the Veda texts known also as the Upanishads. The name is a morphophonological form of Veda-anta = "Veda-end" = "the appendix to the Vedic hymns." It is also speculated that "Vedānta" means "the purpose or goal...

. By his scintillating intellectual brilliance, powerful oratory, magnetic personality, sincerity of purpose, indomitable will, purity of thought, and loftiness of character he took the entire intellectual and religious class by storm.

Shankaracharya of Govardhan Math

Around the time the Swami became Shankaracharya of Sharada Peetha, the Shankaracharya of Govardhan Math Puri, Jagadguru Śankarācārya Sri Madhusudhan Tirtha, was in failing health and was greatly impressed by Bharati Krishna Tirtha. Madhusudan Tirtha requested Bharati to succeed him at the Govardhan Math, however the Swami respectfully declined the offer. However, in 1925, Śankarācārya Sri Madhusudhan Tirtha's health took a serious turn and Swami Bhārāti Kṛṣṇa Tirtha had to accept the Govardhan Math's Gadi. In 1925, Swami Bhārāti Kṛṣṇa Tirtha assumed the pontificate of Shankaracharya of Govardhan Math, Puri
Puri
Puri is district headquarter, a city situated about south of state capital Bhubaneswar, on the eastern coast of the Bay of Bengal in the Indian state of Orissa. It is also known as Jagannath Puri after the Jagannath Temple . It is a holy city of the Hindus as a part of the Char Dham pilgrimages...

 and relinquished the pontificate of Sharadapeeth Gadi of Sringeri. He installed Sri Swarupanandji as the new Shankaracharya of Sharada Peetha.

Jagadguru

After becoming the Shankaracharya of Govardhan Math, Swami Bharati toured all over the world for 35 years to spread the values of peace, harmony and brotherhood and to spread the message of the Sanātana Dharma. He took upon himself the colossal task of the renaissance of Indian culture.

While being a pontiff, he wrote a large number of treatises and books on religion
Religion
Religion is a collection of cultural systems, belief systems, and worldviews that establishes symbols that relate humanity to spirituality and, sometimes, to moral values. Many religions have narratives, symbols, traditions and sacred histories that are intended to give meaning to life or to...

, sciences, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, world peace
World peace
World Peace is an ideal of freedom, peace, and happiness among and within all nations and/or people. World peace is an idea of planetary non-violence by which nations willingly cooperate, either voluntarily or by virtue of a system of governance that prevents warfare. The term is sometimes used to...

 and social
Social
The term social refers to a characteristic of living organisms...

 issues. In 1953, at Nagpur, he founded an organization called "Sri Vishwa Punarnirmana Sangha" (World Reconstruction Association). Initially, the administrative board consisted of Jagadguruji's disciples, devotees and admirers of his spiritual ideals for humanitarian service, but later many distinguished people started to contribute to the mission. The Chief Justice
Chief Justice
The Chief Justice in many countries is the name for the presiding member of a Supreme Court in Commonwealth or other countries with an Anglo-Saxon justice system based on English common law, such as the Supreme Court of Canada, the Constitutional Court of South Africa, the Court of Final Appeal of...

 of India
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...

, Justice B.P. Sinha served as its President. Dr. C. D. Deshmukh, the ex-Finance Minister of India and ex-Chairman of the University Grants Commission served as its Vice-President.

In February 1958 he went on a trans-oceanic tour to America to speak on world peace and Vedanta, staying three months in Los Angeles, California traveling via the United Kingdom. This was the first tour outside India by a Shankaracharya in the history of the order. The tour was sponsored by Self-Realization Fellowship
Self-Realization Fellowship
Self-Realization Fellowship / Yogoda Satsanga Society of India is a worldwide spiritual organization founded by Paramahansa Yogananda in 1920 and based in Mount Washington in Los Angeles, California....

 of Los Angeles, the Vedantic Society founded by Paramhansa Yogananda in America.

He attended many national and international religious conferences and many other yoga workshops. He believed in the Vedantic ideal of "Pūrnatva" which literally translated means, "all-round perfection
Perfection
Perfection is, broadly, a state of completeness and flawlessness.The term "perfection" is actually used to designate a range of diverse, if often kindred, concepts...

 and harmony". He remained the Shankaracharya of the Govardhan Matha until his death in 1960.

In 1965 a Chair of Vedic Studies was founded at Banares Hindu University by Shri Arvind N. Mafatlala, a generous Mumbai business magnate and math devotee of the late Swami Sankaracarya.

Mathematics

Jagadguru Swami Sri Bhārāti Kṛṣṇa Tirthaji Maharaja's book "Vedic Mathematics" opened the floodgates of similar literature, often derived from the Swami's 16 Sūtras themselves. His treatise is a regards speed and accuracy in basic mathematics. The Vedic Math ideal is a mental calculation and one-line notation.

The foundations of Vedic Mathematics were mentioned in the Vedas
Vedas
The Vedas are a large body of texts originating in ancient India. Composed in Vedic Sanskrit, the texts constitute the oldest layer of Sanskrit literature and the oldest scriptures of Hinduism....

 themselves and even in the Vedanta
Vedanta
Vedānta was originally a word used in Hindu philosophy as a synonym for that part of the Veda texts known also as the Upanishads. The name is a morphophonological form of Veda-anta = "Veda-end" = "the appendix to the Vedic hymns." It is also speculated that "Vedānta" means "the purpose or goal...

 scriptures. These had lain unused for many millennia, till the Swami rediscovered them.

His book, Vedic Mathematics, comprises many algorithms. He revealed his source in the ancient Hindu Vedas. Some are intuitively reconstructed from the Atharva Veda and from Parisistas (appendix) of the Atharva Veda. "The Upaveda of Sthapatya (engineering) comprises all kinds of architectural and structural human endeavor and all visual arts (and mathematics)." His work seems to be a whole Parisistas (appendix) itself.

The ancient Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...

 writers did not use numerals when writing big numbers but preferred to use the letters of the Sanskrit Devanāgarī
Devanagari
Devanagari |deva]]" and "nāgarī" ), also called Nagari , is an abugida alphabet of India and Nepal...

 alphabet. In the Vedic Sūtras the key word steps to solving many problems are given in a terse, decimal code of certain sets of rhyming syllables, within the verses of the Sūtra. The fact that the alphabetic code is in the natural order and can be immediately interpreted, is clear proof that the code language was resorted not for concealment but for greater ease in verification.

The Swami had written sixteen volumes on the Vedic Mathematics field explaining all the topics of mathematical study. Alas, many advanced formula were promised but not given in his first and only book. After his 1956 life's work manuscript on Vedic mathematics was lost in a fire at the home of a disciple, though he was going blind from cataract
Cataract
A cataract is a clouding that develops in the crystalline lens of the eye or in its envelope, varying in degree from slight to complete opacity and obstructing the passage of light...

s, he re-wrote the manuscript in 1957 in six weeks. It was to be proofread and published in the USA but was send back to India in 1960 after his death. In 1965, this manuscript was published by Motilal Banarsidass, Varanasi, India and reprinted four times in the 1970s.

His book, Vedic Mathematics, included sixteen terse formulas for mental mathematics. For arithmetic, we are given several algorithms for whole number multiplication and division, (flag or straight) division, fraction conversion to repeating decimal numbers, calculations with measures of mixed units, summation of a series, squares and square roots (duplex method), cubes and cube roots (with expressions for a digit schedule), and divisibility (by osculation).

He gives a poem in Anusub metre, couched in the alphabetic Code-Language that has three meanings, a hymn to Lord Srī Kṛṣṇa, a hymn in praise of the Lord Shri Shankara, and the third the value of pi/10 to 32 decimal places, pi/10 = 0.31415926535897932384626433832792... with a "self-contained master-key" for extending the evaluation to any number of decimal places.

Several tests and techniques for factoring and solving certain algebraic equations with integer roots for quadratic, cubic, biquadratic, pentic equations, systems of linear equations, and systems of quadratic equations are demonstrated. For fractional expressions, a separation algorithm and fraction merger algorithms are given. Other techniques handle certain patterns of some special case algebraic equations. Just an introduction to differential and integral calculus is given.

Geometric applications are reviewed for linear equations, analytic conics, the equation for the asymptotes, and the equation to the conjugate-hyperbola. Five simple geometric proofs for the Pythagorean theorem
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...

 are given. A 5-line proof of Apollonius' theorem
Apollonius' theorem
In geometry, Apollonius' theorem is a theorem relating the length of a median of a triangle to the lengths of its side.Specifically, in any triangle ABC, if AD is a median, thenAB^2 + AC^2 = 2\,...

 is given.

Advanced topics promised included the integral calculus (the center of gravity of hemispheres, conics), trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

, astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

 (spherical triangles, earth's daily rotation, earth's annual rotation about the sun and eclipses), and engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

(dynamics, statics, hydrostatics, pneumatics, applied mechanics).

In his final comments he asserted that the names for "Arabic numerals," "Pythagoras' Theorem," and "Cartesian" co-ordinates are historical misnomers.

External links

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