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

Desargues' Theorem

Desargues' theorem states that two triangles are in perspective axially if and only if they are in perspective centrally. Corresponding sides of the triangles, when extended, meet at points on a line called the axis of perspectivity. The lines which run through corresponding vertices on the triangles meet at a point called the center of perspectivity. Desargues's theorem states that the truth of the first condition is necessary and sufficient for the truth of the second.

Desargues' theorem

Play around with Desargues

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

Dobble card trick with Desargues's Theorem

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

Drag the cards from the cards containers into the circles(points) on the lines and triangles. You can click on 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 Desargues-Dobble playing!

CARDS:

SYMBOLS: