Part I: Introduction Dobble: the basics Getting started: Levels 2 and 3 Card-symbol duality Complete Dobble systems Levels 4 and 5
Part II: Dobble and geometry The basic connection A 7×7 ‘computer game’ geometry Card display: a 7×7 Dobble grid Completing the set: Slope cards A three-dimensional perspective ‘Infinite Dobble’
Part III: Geometry card tricks Pappus’s theorem (card trick 1) Desargues’ theorem (card trick 2) Orthogonality (card trick 3) Altitudes of a triangle (card trick 4)
Part IV: Finite projective planes Dobble systems and FPPs Known and unknown Dobble systems Symmetries of Dobble systems Card display: a Singer cycle Subplanes and ‘Happy Families’
Part V: Block designs and their applications Block designs Experiment design Error-correcting codes

Pappus's Theorem

Pappus's theorem states that given one set of collinear points A,B,C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear, lying on the Pappus line.

Pappus theorem image

Play around with Pappus

Use the following applet produced in GeoGebra to play around the with the points on the lines to see Pappus's theorem in action.

Dobble card trick with Pappus Theorem

Let's try Pappus's Theorem with Level 5 Dobble!

Drag the cards from the cards containers into the black circle(points) on the lines. You can click a card to see which symbols it conatins and click on two cards to see the common symbol of the two. Similarly, you can click on a symbol to highlight the cards that contains that symbol and click on two symbols to see a card that contains both of those symbols.

Happy Pappus-Dobble playing!

CARDS:

SYMBOLS: