As a brief introduction to the content and format of *Fare mathematica* some excerpts are given in English translation:

**The Table of Contents from the Students’ Volume**:

**CONTENTS**

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**Preface** by** **Fulvia Furinghetti

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**Introduction** for students.

**CHAPTER 1: FROM ARITHMETIC TO ALGEBRA - Numeration**: Egyptians; Babylonians; Greeks; Romans; Mayas; Indians, at last; Who invented binary numbers? - **Operations and non-negative integers**:** **Middle Ages and Renaissance - **Not only non-negative numbers**:** **Fractions in Egypt: the Horus’ eye; How Egyptians wrote fractions; Decimals and Arabs; Decimals in Europe - **The arithmetic triangle:** Chinese, Arabs, Europeans… - **Curious problems:** Let’s solve together; Other problems: the text; Other problems: the solutions - **“False” numbers:** In sixteenth-century Italy; A woman grapples with mathematics - **From words to symbols:** A great Arabian mathematician; Diophantus left a mark; All of them are equations; A “recipe” to solve an equation; The science of “literal calculus”; Philosopher, physician and… mathematician - **Problems and equations:** Linear and quadratic problems - **Bombelli and the number i**:

**CHAPTER 2 – FACES OF GEOMETRY - Arithmetic and geometry: figurate numbers**:** **Polygonal numbers; Pythagorean terns; Ingenious ways to obtain Pythagorean terns - **Pythagorean theorem**: A walk through history: sides and squares…; … a problem in the Renaissance…; …problems and equations - **Far points**: About towers and other buildings; How to bore a tunnel and not come out in the wrong place - **S****quare root of 2**: How did they do it? - **pi**: What is the true value? - **Archimedes**: A volley of propositions; The area of the circle and the method of *exhaustion -* **Cartesian coordinates?…**: In the fourteenth century; One of the fathers - **Geometry, of Euclid and not**: An authoritative introduction, but…; The *Elements*: almost a Bible; Two millennia later - **Trigonometry**:** **From a sixteenth-century book - **What is topology?**:** **A new geometry; The problem of Königsberg’s bridges; The explanation of Euler - **And more… solid numbers**.

**CHAPTER 3: THEMES OF MODERN MATHEMATICS - Logic: an ancient but current science**:** **What are logical connectives?; The art of… reasoning; Mathematics takes possession of logic - **Logic to build numbers**:** **Gottlob Frege and Bertrand Russell - **Let’s measure uncertainty**: Galileo and a problem about the casting of three dice; Epistolary interchanges; The classical conception of probability; Other conceptions of probability - **Infinity**:** **Runners, arrows, hares, tortoise,…; The whole is not greater than the part; Infinite is a source of other paradoxes; Let’s arrange our knowledge - **Cantor’s paradise**:** **Real numbers are more than integers; Cantor in Hilbert’s opinion - **Infinitesimals before Newton**:** **The circle; The torus; The indivisibles - **Limits, derivatives, integrals** (I’m sorry if it is too little): Isaac Newton - **We don’t stop… history continues…**

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