" With poignancy and audacity, Frame builds an unexpected bridge between mathematical beauty and human sorrow, illuminating both." —Francis Su, author of Mathematics for Human FlourishingWe all know the euphoria of intellectual epiphany—the thrill of sudden understanding. But coupled with that excitement is a sense of loss: a moment of epiphany can never be repeated. In Geometry of Grief *,*mathematician Michael Frame draws on a career's worth of ...

A mathematician and a poet explore fractals as they appear in nature, art, medicine, and technology in this "instant classic" introduction (David Peak, Utah State University)." Fractal Worlds portrays math as math lovers know it: a beautiful garden, a place of curiosity and delight, a tribute to human creativity and the wonders of nature." —Steven Strogatz, author of Sync

Cosa lega l'irreversibilità della morte all'irreversibilità di una scoperta illuminante? Come può la geometria frattale aiutarci a superare il dolore di una perdita? Un oggetto viene definito frattale quando ripete se stesso su scale diverse, in un'iterazione che produce forme complesse e affascinanti. Allo stesso modo, Michael Frame propone una visione del tutto nuova dell'esperienza del dolore, costruendo un modello secondo cui all'interno di grandi perdite si annidano perdite minori, tu...

An award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciencesThis is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers essential ideas and theories of basic calculus and probability while providing examples of how they apply to subjects like chemotherapy and tumor growth, chemical diffusion, allometric scaling, pre...

Volume Two of an award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciencesThis is the second of a two-part series exploring essential concepts of calculus in the context of biological systems. Building on the essential ideas and theories of basic calculus taught in Mathematical Models in the Biosciences I, this book focuses on epidemiological models, mathematical foundations of virus ...

【推薦人】洪萬生 國立臺灣師範大學數學系退休教授蘇益賢 臨床心理師蘇絢慧 諮商心理師／璞成健康心理學堂創辦人以幾何學思考人生有種美好且形而上的領悟我們有時會感受到，對某事突然理解或頓悟而產生的瞬間快感，但伴隨著興奮之後的是一種失落感，因為領悟的剎那永遠不會重複，也就是幾何學談的「不可逆轉」，我們對此情境變化的反應就是悲傷。但對《悲傷幾何學》作者而言，悲傷可能是人們生命中充滿可能性的時刻，讓我們能夠了解，失去親人或生命中各種事物，與失去頓悟的快感之間有相似之處。透過幾何學的放大對稱性，我們依然會看到原始形狀。同樣的，鑲嵌在大損失中的是較小的損失。這種領悟有助於減輕人生痛苦，重新定向我們的思維。作者認為，悲傷有兩種意思。首先，悲傷是對永久失去的反應：它是不可逆轉、帶有情感重量，且是超凡的；此外，悲傷是自我相似：譬如，喪母之痛包含許多「比較輕微」的悲傷，因為再也不能促膝長談，或一起用餐、散步。然而，每一個微小悲傷都是對失去母親的反應之縮影，可以當成尋找有...

This is a collection of articles, many written by people who worked with Mandelbrot, memorializing the remarkable breadth and depth of his work in science and the arts. Contributors include mathematicians, physicists, biologists, economists, and engineers, as expected; and also artists, musicians, teachers, an historian, an architect, a filmmaker, and a comic. Some articles are quite technical, others entirely descriptive. All include stories about Benoit.Also included are chapters on frac...

This book provides a collection of 44 simple computer and physical laboratory experiments, including some for an artist's studio and some for a kitchen, that illustrate the concepts of fractal geometry. In addition to standard topics — iterated function systems (IFS), fractal dimension computation, the Mandelbrot set — we explore data analysis by driven IFS, construction of four-dimensional fractals, basic multifractals, synchronization of chaotic processes, fractal finger paints, cooking ...

What you see isn’t real. What you hear is a lie. And the truth just started a war.When a presidential candidate confesses to election rigging during a live debate, it should be over. Except she never said those words. The confession was deepfaked in real-time, and it fooled every detection system on Earth.Aegis agents Jordan Hayes and Alex Mercer are called in to hunt the source through a maze of shell companies and false leads. They find their enemy an tak...

Are the Thirty-Nine Articles just dusty relics of the Reformation - or a living treasure for today's church?Michael Jensen and Tom Frame argue the latter. With clarity and conviction, they show how these 450-year-old statements of faith still speak powerfully to the challenges facing Anglicans now. Far from being an awkward historical curiosity, the Articles are rooted in Scripture, brimming with theological insight, and vital for anyone who wants to understand Anglican identity.

In the fifth volume of his groundbreaking work, "Lives of the Most Eminent Painters, Sculptors and Architects," Giorgio Vasari delves into the lives and works of some of the most influential artists of the Italian Renaissance. From the enigmatic Leonardo da Vinci to the masterful Michelangelo, Vasari's vivid prose and meticulous research bring to life the personalities, struggles, and triumphs of these artistic giants. This volume offers a captivating glimpse into the creative minds that s...

The Bible stands at the heart of the Christian faith, but now more than ever many question its historical reliability and relevance for life today. In what may become the definitive contemporary evangelical resource on this foundational topic, John MacArthur and a host of pastors, biblical scholars, historians, and theologians defend the doctrine of biblical inerrancy from their various disciplines. With contributions from evangelical leaders such as Kevin DeYoung, R. Albert Mohler Jr., R....