MATHEMATICS BEGINS WITH A QUESTION
Why does a classic football have exactly 12 pentagons? Can ants discover the shape of their world? And why can’t you comb a sphere?
A journey from familiar objects to ideas that let you see them in a new way.
For curious minds. Not just mathematicians.
THE BOOK
A journey from Euler’s formula to geometry and topology
An ordinary football hides some extraordinary mathematics. The answer to the question about its patches is only the beginning.
Starting with vertices, edges and faces, we explore curved surfaces, mountains and passes, swirling vector fields and points that must stay fixed. A single idea connects these stories: the shape of the whole matters.
Written for curious teenagers and adults, the book uses pictures, questions and thought experiments to explain where mathematical ideas come from.
Preview: introduction and contents in Polish (PDF) ↗THREE QUESTIONS TO START WITH
The number of pentagons in a classic football is more than a designer’s choice.
If a surface has the topology of a sphere, every face is a pentagon or a hexagon, and exactly three faces meet at each vertex, Euler’s formula forces the number of pentagons to be 12.
V − E + F = 2 ⇒ P = 12
Can you discover curvature without ever leaving the surface you live on?
Yes. Measuring distances and angles can reveal curvature. On a sphere, the angles of a triangle bounded by great-circle arcs add up to more than 180 degrees.
On a sphere, a perfect hairstyle is impossible. On a doughnut-shaped surface, things are different.
A sphere has no continuous tangent vector field that is nonzero everywhere. A torus does. The topology of the surface determines whether a perfect “hairstyle” is possible.
MACIEJ STAROSTKA / AUTHORABOUT THE AUTHOR
Maciej Starostka is a mathematician who writes about geometry and topology.
His book presents mathematics as the art of asking questions and discovering connections between seemingly unrelated problems. Pictures and intuition guide the reader from everyday observations to surprising ideas.
“What matters most to me is that, after reading a chapter, you are left with an image and a question.”Translated from the introduction
YOUR JOURNEY STARTS HERE
Explore the English edition, or read the book in Polish.
Purchases take place at the selected bookstore. Please check its website for price and availability.
LET’S TALK ABOUT THE BOOK
For book enquiries, reviews or author events:
maciejstarostka@gmail.com ↗