Products related to Theorem:
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Fermat’s Last Theorem
Introducing the Collins Modern Classics, a series featuring some of the most significant books of recent times, books that shed light on the human experience – classics which will endure for generations to come. ‘Maths is one of the purest forms of thought, and to outsiders mathematicians may seem almost otherworldly’ In 1963, schoolboy Andrew Wiles stumbled across the world’s greatest mathematical problem: Fermat’s Last Theorem.Unsolved for over 300 years, he dreamed of cracking it. Combining thrilling storytelling with a fascinating history of scientific discovery, Simon Singh uncovers how an Englishman, after years of secret toil, finally solved mathematics’ most challenging problem. Fermat’s Last Theorem is remarkable story of human endeavour, obsession and intellectual brilliance, sealing its reputation as a classic of popular science writing. ‘To read it is to realise that there is a world of beauty and intellectual challenge that is denied to 99.9 per cent of us who are not high-level mathematicians’ The Times
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Lectures on the h-Cobordism Theorem
Important lectures on differential topology by acclaimed mathematician John MilnorThese are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University.These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale.Milnor's goal was to provide a fully rigorous proof in terms of Morse functions.This book remains an important resource in the application of Morse theory.
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Lectures on the h-Cobordism Theorem
Important lectures on differential topology by acclaimed mathematician John MilnorThese are notes from lectures that John Milnor delivered as a seminar on differential topology in 1963 at Princeton University.These lectures give a new proof of the h-cobordism theorem that is different from the original proof presented by Stephen Smale.Milnor's goal was to provide a fully rigorous proof in terms of Morse functions.This book remains an important resource in the application of Morse theory.
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Birth of a Theorem : A Mathematical Adventure
“This man could plainly do for mathematics what Brian Cox has done for physics” — Sunday TimesHow does a genius see the world?Where and how does inspiration strike?Cédric Villani takes us on a mesmerising adventure as he wrestles with the Boltzmann equation – a new theorem that will eventually win him the most coveted prize in mathematics and a place in the mathematical history books.Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness. His story is one of courage and partnership, doubt and anxiety, elation and despair.Of ordinary family life blurring with the abstract world of mathematical physics, of theories and equations that haunt your dreams and seeking the elusive inspiration found only in a locked, darkened room. Blending science with history, biography with myth, Villani conjures up an inimitable cast: the omnipresent Einstein, mad genius Kurt Godel, and Villani’s personal hero, John Nash. Step inside the magical world of Cédric Villani…
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What is the Pythagorean theorem and the cathetus theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be written as a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides, called catheti. The cathetus theorem, also known as the converse of the Pythagorean theorem, states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right-angled triangle. In other words, if a^2 + b^2 = c^2, then the triangle is a right-angled triangle, where c is the longest side (hypotenuse) and a and b are
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What is the Pythagorean theorem and the altitude theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as a^2 + b^2 = c^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. The altitude theorem, also known as the geometric mean theorem, states that in a right-angled triangle, the altitude (the perpendicular line from the right angle to the hypotenuse) is the geometric mean between the two segments of the hypotenuse. This can be expressed as h^2 = p * q, where h is the length of the altitude, and p and q are the lengths of the two segments of the hypotenuse.
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How can the altitude theorem and the cathetus theorem be transformed?
The altitude theorem and the cathetus theorem can be transformed by applying them in different geometric shapes and contexts. For example, the altitude theorem, which states that the length of the altitude of a triangle is inversely proportional to the length of the corresponding base, can be applied to various types of triangles and even extended to other polygons. Similarly, the cathetus theorem, which relates the lengths of the two perpendicular sides of a right triangle to the length of the hypotenuse, can be generalized to other right-angled shapes or even applied in three-dimensional geometry. By exploring different scenarios and shapes, these theorems can be adapted and transformed to solve a wide range of geometric problems.
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What are the altitude theorem and the cathetus theorem of Euclid?
The altitude theorem of Euclid states that in a right-angled triangle, the square of the length of the altitude drawn to the hypotenuse is equal to the product of the lengths of the two segments of the hypotenuse. This theorem is also known as the geometric mean theorem. The cathetus theorem of Euclid states that in a right-angled triangle, the square of the length of one of the catheti (the sides that form the right angle) is equal to the product of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that cathetus. This theorem is also known as the Pythagorean theorem. Both the altitude theorem and the cathetus theorem are fundamental principles in the study of geometry and are essential for understanding the properties of right-angled triangles.
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Euler's Pioneering Equation : The most beautiful theorem in mathematics
In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics.Twenty-four theorems were listed and readers were invited to award each a 'score for beauty'.While there were many worthy competitors, the winner was 'Euler's equation'.In 2004 Physics World carried out a similar poll of 'greatest equations', and found that among physicists Euler's mathematical result came second only to Maxwell's equations.The Stanford mathematician Keith Devlin reflected the feelings of many in describing it as "like a Shakespearian sonnet that captures the very essence of love, or a painting which brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence".What is it that makes Euler's identity, eip + 1 = 0, so special?In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most important numbers in mathematics, each associated with a story in themselves: the number 1, the basis of our counting system; the concept of zero, which was a major development in mathematics, and opened up the idea of negative numbers; p an irrational number, the basis for the measurement of circles; the exponential e, associated with exponential growth and logarithms; and the imaginary number i, the square root of -1, the basis of complex numbers.Following a chapter on each of the elements, Robin Wilson discusses how the startling relationship between them was established, including the several near misses to the discovery of the formula.
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Moving Beyond Modern Portfolio Theory : Investing That Matters
Moving Beyond Modern Portfolio Theory: Investing That Matters tells the story of how Modern Portfolio Theory (MPT) revolutionized the investing world and the real economy, but is now showing its age.MPT has no mechanism to understand its impacts on the environmental, social and financial systems, nor any tools for investors to mitigate the havoc that systemic risks can wreck on their portfolios.It’s time for MPT to evolve. The authors propose a new imperative to improve finance’s ability to fulfil its twin main purposes: providing adequate returns to individuals and directing capital to where it is needed in the economy.They show how some of the largest investors in the world focus not on picking stocks, but on mitigating systemic risks, such as climate change and a lack of gender diversity, so as to improve the risk/return of the market as a whole, despite current theory saying that should be impossible. "Moving beyond MPT" recognizes the complex relations between investing and the systems on which capital markets rely, "Investing that matters" embraces MPT’s focus on diversification and risk adjusted return, but understands them in the context of the real economy and the total return needs of investors.Whether an investor, an MBA student, a Finance Professor or a sustainability professional, Moving Beyond Modern Portfolio Theory: Investing That Matters is thought-provoking and relevant.Its bold critique shows how the real world already is moving beyond investing orthodoxy.
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Personal Finance and Investing All-in-One For Dummies
Providing a one-stop shop for every aspect of your money management, Personal Finance and Investing All-in-One For Dummies is the perfect guide to getting the most from your money.This friendly guide gives you expert advice on everything from getting the best current account and coping with credit cards to being savvy with savings and creating wealth with investments.It also lets you know how to save money on tax and build up a healthy pension. Personal Finance and Investing All-In-One For Dummies will cover: Organising Your Finances and Dealing with DebtPaying Less TaxBuilding up Savings and InvestmentsRetiring WealthyYour Wealth and the Next Generation
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Behavioural Investing : A Practitioner's Guide to Applying Behavioural Finance
Behavioural investing seeks to bridge the gap between psychology and investing.All too many investors are unaware of the mental pitfalls that await them.Even once we are aware of our biases, we must recognise that knowledge does not equal behaviour.The solution lies is designing and adopting an investment process that is at least partially robust to behavioural decision-making errors. Behavioural Investing: A Practitioner’s Guide to Applying Behavioural Finance explores the biases we face, the way in which they show up in the investment process, and urges readers to adopt an empirically based sceptical approach to investing.This book is unique in combining insights from the field of applied psychology with a through understanding of the investment problem.The content is practitioner focused throughout and will be essential reading for any investment professional looking to improve their investing behaviour to maximise returns.Key features include: The only book to cover the applications of behavioural financeAn executive summary for every chapter with key points highlighted at the chapter startInformation on the key behavioural biases of professional investors, including The seven sins of fund management, Investment myth busting, and The Tao of investingPractical examples showing how using a psychologically inspired model can improve on standard, common practice valuation toolsWritten by an internationally renowned expert in the field of behavioural finance
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What is Thales' theorem?
Thales' theorem states that if A, B, and C are points on a circle where the line AC is a diameter, then the angle at B is a right angle. In other words, if a triangle is inscribed in a circle with one of its sides being the diameter of the circle, then that triangle is a right triangle. Thales' theorem is a fundamental result in geometry and is named after the ancient Greek mathematician Thales of Miletus.
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What is the difference between similarity theorem 1 and similarity theorem 2?
Similarity theorem 1, also known as the Angle-Angle (AA) similarity theorem, states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. On the other hand, similarity theorem 2, also known as the Side-Angle-Side (SAS) similarity theorem, states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar. The main difference between the two theorems is the criteria for establishing similarity - AA theorem focuses on angle congruence, while SAS theorem focuses on both side proportionality and angle congruence.
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What is the proof for the altitude theorem and the cathetus theorem?
The altitude theorem states that in a right triangle, the altitude drawn from the right angle to the hypotenuse creates two similar triangles with the original triangle. This can be proven using the properties of similar triangles and the Pythagorean theorem. The cathetus theorem states that the two legs of a right triangle are proportional to the segments of the hypotenuse that they create when an altitude is drawn from the right angle. This can also be proven using the properties of similar triangles and the Pythagorean theorem.
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What is the formula for the altitude theorem and the cathetus theorem?
The formula for the altitude theorem is: \( a^2 = x \cdot (x + h) \), where \( a \) is the length of the hypotenuse, \( x \) is the length of one of the legs, and \( h \) is the length of the altitude drawn to the hypotenuse from the right angle. The formula for the cathetus theorem is: \( x \cdot y = h^2 \), where \( x \) and \( y \) are the lengths of the two legs of the right triangle, and \( h \) is the length of the altitude drawn to the hypotenuse from the right angle.
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