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Numerous photographs and diagrams help explain and illustrate mathematical phenomena in this series of thought-provoking expositions. Ranging from simple puzzles and games to more advanced problems, topics include the psychology of lottery players, the arrangement of chromosomes in a human cell, new and larger prime numbers, the fair division of a cake, how to find the shortest possible way to link a dozen locations by rail, and many other absorbing conundrums. A fascinating glimpse into the world of numbers and their uses. 1969 ed. 391 b/w illus.
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Customer Reviews (2)

One step beyond Martin Gardner
Among the top 3 recreational math books I have read.Multiple mathematical problems are tackled with a pithy style suitable to recreational mathematicians who want to go beyond the lyricism of Martin Gardner.

Mathematical Snapshots
Mathematical Snapshots is a wonderful excursion into the mind of a mathematician.It answers a question that was asked of the author "You claim to be a mathematician; well, what does one do all day when one is amathematician?"This book explores games, the computation of shortestpaths, why two soap bubbles blown from the same pipe are different sizes,how to pursue another boat on the open water, how to color maps, thesimplest forms of solid objects, mobius strips, where to locate schools,the ideal musical scale, and many, many others.Each topic is presented ina short, concise paragraph along with a diagram or picture of explanation. The author asks the reader to supply answers and reasoning.It is readilyreadable by those with mathematical inclination (even if they can no longer`push' the numbers) and provides hours of enjoyment and expansion of themind. ... Read more

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A stimulating collection of one hundred problems, complete with instructive solutions, on numbers, equations, polygons, polyhedra and many other topics. Extremely challenging for anyone with a fair knowledge of mathematics up to calculus. Includes an additional 13 problems without solutions.
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Chapters: Stanislaw Ulam, Roald Hoffmann, Billy Wilder, Shmuel Yosef Agnon, Karl Radek, Hugo Steinhaus, Melanie Klein, Zalman Schachter-Shalomi, Moise Kisling, Isaac Deutscher, Alexander Beliavsky, Lee Strasberg, Jacob Frank, Eliot Spitzer, Moses Schorr, Simon Wiesenthal, Leo Birinski, Martin Buber, Eric Kandel, Łucja Frey, Abba Hushi, Richard Von Mises, Salo Flohr, Bruno Schulz, Robert Kronfeld, Henryk Grossman, Jacob Itzhak Niemirower, Franciszek Zachara, Mordechai Rokeach, Edmond Wilhelm Brillant, Arthur Hertzberg, Arthur Frank Burns, Ben Zion Halberstam, Helena Rubinstein, Aharon Rokeach, Muhammad Asad, Lewis Bernstein Namier, Salomon Buber, Meir Balaban, Elimelech of Lizhensk, Israel Zolli, Isidor Isaac Rabi, Daniel Yanofsky, Ira Schnapp, Alicia Appleman-Jurman, Samuel Yellin, Emanuel Feuermann, Joseph Roth, František Kriegel, Salo Landau, Moses Horowitz, Chaim Elazar Spira, Walter Krivitsky, Mikhail Fridman, Julia Brystiger, Adam Daniel Rotfeld, Efraim Racker, Ostap Ortwin, Adam Ulam, Mieczysław Horszowski, David Josef Bach, Mordechai Gebirtig, Siegmund Glücksmann, Joseph Samuel Bloch, Aryeh Leib Hacohen Heller, Avigdor Aptowitzer, Nahman Avigad, Morris Gutstein, Joshua Falk, Stanisław Jerzy Lec, Nachman Krochmal, Leo Aryeh Mayer, Salo Wittmayer Baron, Hersch Lauterpacht, Max Margules, Henry Roth, Manfred Sakel, Jakub Karol Parnas, Yitzchok Yaakov Weiss, Elisabeth Bergner, Ignaz Friedman, List of Galician Jews, Emanuel Ax, Heinrich Schenker, Michael Dorfman, Rose Rand, Moshe Teitelbaum, Max Judd, Simhah Pinsker, Leopold Trepper, Wiktor Brillant, Isaac Erter, Kalman Kahana, Adolf Beck, Georges Charpak, Izak Aloni, Haim Nathan Dembitzer, Edward Gerstenfeld, Velvel Zbarjer, Leopold Infeld, Yissachar Dov Rokeach, Rena Kornreich Gelissen, Dov Berish Weidenfeld, Salomon Bochner, Josef Gerstmann, Maurycy Gottlieb, Cecilia Krieger, Oscar Chajes, Gideon Hausner, Solomon Judah Loeb Rapoport, Naftali Herz Tur-Sinai, Iuliu Baras...More: http://booksllc.net/?id=21378255 ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Wacław Sierpiński, Stefan Banach, Kazimierz Kuratowski, Hugo Steinhaus, Edward Flatau, George Zarnecki, Jerzy Kuryłowicz, Stanisław Kutrzeba, Emil Godlewski, Andrzej Gawroński, Jerzy Strzelczyk, Kazimierz Bartel, Antoni Zygmund, Zygmunt Wojciechowski, Gustaw Holoubek, Tadeusz Banachiewicz, Henryk Samsonowicz, Władysław Konopczyński, Benedykt Dybowski, Szymon Askenazy, Oskar Halecki, Karol Lanckoroński, Gerard Labuda, Stanisław Lorentz, Adam Chętnik, Maria Janion, Henryk Łowmiański, Kazimierz Piwarski, Wacław Sobieski, Stanisław Salmonowicz. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Stefan Banach ( listen) (18921945) was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. A self-taught mathematics prodigy, Banach was the founder of modern functional analysis and a founder of the Lwów School of Mathematics. Among his most prominent achievements was the 1932 book, Théorie des opérations linéaires (Theory of Linear Operations), the first monograph on the general theory of linear-metric space. Notable mathematical concepts named after Banach include the BanachTarski paradox, HahnBanach theorem, BanachSteinhaus theorem, Banach-Mazur game and Banach space. Stefan Banach was born on March 30, 1892, at St. Lazarus General Hospital in Kraków, then part of Austro-Hungarian Galicia. Banach's parents were Stefan Greczek and one Katarzyna Banach, both natives of the Podhale region. Stefan Greczek was born in Ostrowsko near the town of Nowy Targ and at one time was a soldier in the Austro-Hungarian Army stationed in Kraków. Stefan Greczek's father, Józef, was a farmer and a village mayor and Józef's wife, Antonina (née Borkowska) bore the Pomian coat of arms. Banach's mother left him after baptizing him when he was four days old. Her name on the bi...More: http://booksllc.net/?id=29646 ... Read more

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Chapters: Members of the Lwów Scientific Society, Marie Curie, Stefan Banach, Hugo Steinhaus, Ignacy Mościcki, Moses Schorr, Rudolf Weigl, Jan Niecisław Baudouin de Courtenay, Aleksander Brückner, Kazimierz Twardowski, Leon Kozłowski, Stanisław Kutrzeba, Kazimierz Bartel, Jan Czekanowski, Tadeusz Stefan Zieliński, Juliusz Kleiner, Benedykt Dybowski, Roman Longchamps de Bérier, Oskar Halecki, Henryk Arctowski, Michael Bobrzynski, Józef Kallenbach, Władysław Abraham, Oswald Balzer, Władysław Natanson. Source: Wikipedia. Pages: 114. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Moses Schorr, Polish: Mojesz Schorr (May 10, 1874 July 8, 1941) was a Rabbi, Polish historian, politician, Bible scholar, assyriologist and orientalist. Schorr was one of the top experts in the scientific life of Galician and Polish Jewry. He was also the first Jewish researcher of Polish archives, historical sources and pinkasim, a noted Assyriologist, the president of the 13th district Bnai Brith Poland, a humanist and reform rabbi who ministered the central synagogue of Poland during its last years before the Nazi annihilation. The range of Moses Schorr's interdisciplinary scholarship is astonishing. Schorr was the first historian who undertook the systematic study of Jewish history in Poland, and Galicia in particular. He made discoveries after finding and translating Babylonian, Assyrian and Hittite legislative annals. As a scholar of the jurisprudence and civilizations of the Ancient Middle East, Schorr can be considered a legal philosopher and sociologist of Ancient Middle Eastern societies. Schorr was personally appointed to the Polish Senate by Polish president Ignacy Mocicki (19261939). Schorr did not belong to any political party, although he was inclined to Zionism. He was active in the social, public a...More: http://booksllc.net/?id=10261403 ... Read more

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Chapters: Members of the Polish Academy of Learning, Wacław Sierpiński, Stefan Banach, Kazimierz Kuratowski, Hugo Steinhaus, Edward Flatau, George Zarnecki, Jerzy Kuryłowicz, Stanisław Kutrzeba, Emil Godlewski, Andrzej Gawroński, Jerzy Strzelczyk, Kazimierz Bartel, Antoni Zygmund, Zygmunt Wojciechowski, Gustaw Holoubek, Tadeusz Banachiewicz, Henryk Samsonowicz, Władysław Konopczyński, Benedykt Dybowski, Szymon Askenazy, Oskar Halecki, Karol Lanckoroński, Gerard Labuda, Stanisław Lorentz, Adam Chętnik, Maria Janion, Henryk Łowmiański, Kazimierz Piwarski, Wacław Sobieski, Stanisław Salmonowicz. Source: Wikipedia. Pages: 101. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Stefan Banach ( listen) (18921945) was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. A self-taught mathematics prodigy, Banach was the founder of modern functional analysis and a founder of the Lwów School of Mathematics. Among his most prominent achievements was the 1932 book, Théorie des opérations linéaires (Theory of Linear Operations), the first monograph on the general theory of linear-metric space. Notable mathematical concepts named after Banach include the BanachTarski paradox, HahnBanach theorem, BanachSteinhaus theorem, Banach-Mazur game and Banach space. Stefan Banach was born on March 30, 1892, at St. Lazarus General Hospital in Kraków, then part of Austro-Hungarian Galicia. Banach's parents were Stefan Greczek and one Katarzyna Banach, both natives of the Podhale region. Stefan Greczek was born in Ostrowsko near the town of Nowy Targ and at one time was a soldier in the Austro-Hungarian Army stationed in Kraków. Stefan Greczek's father, Józef, was a farmer and a village mayor and Józef's wife, Antonina (née Borkowska) bore the Pomian coat of arms. Banach's mother left him after bap...More: http://booksllc.net/?id=29646 ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Stanislaw Ulam, Kazimierz Kuratowski, Benoît Mandelbrot, Alfred Tarski, Hugo Steinhaus, Vilna Gaon, Samuel Eilenberg, Emil Leon Post, Hayyim Selig Slonimski, Mark Kac, Szolem Mandelbrojt, Nachman Aronszajn, Juliusz Schauder, Edward Marczewski, Adolf Lindenbaum, Herman Auerbach, Samuel Dickstein, Mojżesz Presburger. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Alfred Tarski (January 14, 1901, Warsaw, Poland, Russian Empire October 26, 1983, Berkeley, California) was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of California, Berkeley, from 1942 until his death. A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy. Tarski's student Robert Vaught ranked Tarski as one of the four greatest logicians of all time, along with Aristotle, Kurt Gödel, and Gottlob Frege, although Tarski himself expressed great admiration for Charles Sanders Peirce. His biographers Anita and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models." Alfred Tarski was born Alfred Teitelbaum (Polish spelling: "Tajtelbaum"), to parents who were Polish Jews in comfortable circumstances. He first manifested his mathematical abilities while in secondary school, at Warsaw's Szkoa Mazowiecka. Nevertheless, he entered the University of Warsaw in 1918 int...More: http://booksllc.net/?id=59920 ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Marie Curie, Stefan Banach, Hugo Steinhaus, Ignacy Mościcki, Moses Schorr, Rudolf Weigl, Jan Niecisław Baudouin de Courtenay, Aleksander Brückner, Kazimierz Twardowski, Leon Kozłowski, Stanisław Kutrzeba, Kazimierz Bartel, Jan Czekanowski, Tadeusz Stefan Zieliński, Juliusz Kleiner, Benedykt Dybowski, Roman Longchamps de Bérier, Oskar Halecki, Henryk Arctowski, Michael Bobrzynski, Józef Kallenbach, Władysław Abraham, Oswald Balzer, Władysław Natanson. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Moses Schorr, Polish: Mojesz Schorr (May 10, 1874 July 8, 1941) was a Rabbi, Polish historian, politician, Bible scholar, assyriologist and orientalist. Schorr was one of the top experts in the scientific life of Galician and Polish Jewry. He was also the first Jewish researcher of Polish archives, historical sources and pinkasim, a noted Assyriologist, the president of the 13th district Bnai Brith Poland, a humanist and reform rabbi who ministered the central synagogue of Poland during its last years before the Nazi annihilation. The range of Moses Schorr's interdisciplinary scholarship is astonishing. Schorr was the first historian who undertook the systematic study of Jewish history in Poland, and Galicia in particular. He made discoveries after finding and translating Babylonian, Assyrian and Hittite legislative annals. As a scholar of the jurisprudence and civilizations of the Ancient Middle East, Schorr can be considered a legal philosopher and sociologist of Ancient Middle Eastern societies. Schorr was personally appointed to the Polish Senate by Polish president Ignacy Mocicki (19261939). Schorr did not belong to any political party, although he was inclined to Zionism. He was active in the social, public and religious life of Polish Jews, and was often chose...More: http://booksllc.net/?id=10261403 ... Read more

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Chapters: Wac?aw Sierpi?ski, Hugo Steinhaus, Jan W?glarz, Hilary Koprowski, Jerzy Kury?owicz, Jerzy Neyman, Aleksander Wolszczan, Antoni Zygmund, Zygmunt Wojciechowski, Stanis?aw Mazur, Stefan Kieniewicz, Karol My?liwiec, W?adys?aw Markiewicz, Jerzy Samp, Polish Language Council, Edmund Wnuk-Lipi?ski, Fundamenta Mathematicae, Kazimierz Piwarski, Space Research Centre, Unipress, Polish Institute of Physical Chemistry, Sylwester Kaliski. Source: Wikipedia. Pages: 69. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Hilary Koprowski (born December 5, 1916, in Warsaw, Poland) is a Polish virologist and immunologist, and inventor of the world's first effective live polio vaccine. Koprowski, Warsaw, 2007Hilary Koprowski grew up in Warsaw where he attended the Liceum Ogólnoksztacce and from age twelve took piano lessons at the Warsaw Conservatory. He received his medical degree from the Faculty of Medicine at Warsaw University in 1939. He also received music degrees from the Warsaw Conservatory and, in 1940, from the Santa Cecilia Conservatory in Rome. He adopted scientific research as his life's work, though he never gave up music and composed several musical works. In 1939, after the Nazi invasion of Poland Koprowski and his wife Irena, a medical doctor, fled first to Rome, then in 1940 to Paris and finally, via Spain and Portugal, to Brazil, where Koprowski worked in Rio de Janeiro for the Rockefeller Foundation. His field of research for several years was finding a live-virus vaccine against yellow fever. After World War II the Koprowskis settled in Pearl River, New York, where Koprowski was hired as a researcher for Lederle Laboratories, the pharmaceutical division of American Cyanamid. Here Koprowski began his polio experiments which ultimately led to the discovery of the first oral polio v...More: http://booksllc.net/?id=1063891 ... Read more

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Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Alvin Plantinga, Knute Rockne, Hugo Steinhaus, Karl Menger, Paul Erdős, Tariq Ramadan, Vittorio Hösle, Kevin Hart, Douglas Kmiec, Donald Gutierrez, Henri Nouwen, Alasdair Macintyre, John Howard Yoder, Charles P. Neill, Jaegwon Kim, Richard Mcbrien, Dan Lipinski, Moonis Ahmar, John Finnis, Peter Van Inwagen, John P. Meier, James Tabor, John Joseph Haldane, Steven Schwarzschild, G. Robert Blakey, Ralph Mcinerny, Maurice Francis Egan, Nick Trakakis, Albert-László Barabási, Theodore Hesburgh, Charles Malik, John I. Jenkins, Amitabh Mattoo, Edward Malloy, Thomas V. Morris, Yozo Matsushima, Drago Kolar, Charles E. Rice, Alejandro Foxley, Mar Sarhad Yawsip Jammo, Henry H. Carter, Ruth Abbey, Christopher Hollis, Mark Noll, Julius Nieuwland, Daniel J. Myers, Stanley Hauerwas, Bei Dao, Pablo Eisenberg, Rose Rand, Bernard Lander, Elliot R. Wolfson, John T. Noonan, Jr., Anne Norton, Theodor Paleologu, Ernan Mcmullin, Cristina Bicchieri, Jack Miller, Yves Simon, Nathan O. Hatch, David N. Livingstone, Geoffrey Wainwright, John Augustine Zahm, Christian Smith, George Marsden, Virgilio Elizondo, Juan E. Méndez, Robert Audi, Allan Stitt, John L. Kelley, Yum-Tong Siu, Bruce L. Gordon, Laurence Thomas, James Gahagan, Michael Slinger, M. Brian Blake, Malaquías Montoya, Catherine Lacugna, Arnold Ross, Alan Gallay, Carol Ann Mooney, William K. Kelley, George A. Lopez, Gustavo Gutiérrez, Bill Slavick, Eugene Guth, John Paul Lederach, Frank P. Incropera, Asma Afsaruddin, Eugene Ulrich, Guillermo O'donnell, John Logan, Philip Mirowski, Pinchas Hacohen Peli, Dudley G. Wooten, Wladimir Seidel, Matthew V. Storin, Donald T. Critchlow, Paul F. Bradshaw, Rufus Isaacs, John Ferguson, Kenneth Francis Ripple, Thomas F. Konop, Karl-Ludwig Kratz, Janet E. Smith, Michael Joncas, John Henry Morgan, Donald George Vogl...More: http://booksllc.net/?id=584063 ... Read more