Geometry card tricks

There are many mathematical theories that can be explored within the world of Dobble. In this page, there are some of those geometries and theories you can learn about, while playing around with the interactive applets and games.

Pappus' Theorem

Pappus' theorem states that let A, B, and C be a set of three collinear points and let X, Y, and Z be set of collinear points. If the lines AY, BZ, and CX intersect the lines BX, CY, and AZ, respectively, then the three points of intersection are collinear, on the Pappus line.

Play around with Pappus

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

Dobble card trick with Pappus Theorem

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

Here, think of the Dobble cards as points. Therefore, the cards are collinear if they have a common symbol.

Try to find the intersection points on the Pappus line. Hint: the card on a intersection point would have the common symbols from both (dotted) lines that intersect there. Drag the cards from the cards containers into the black circle(points) on the lines. Try using as different cards as possible but sometimes you may have to repeat cards.

Disclaimer: if you are using Google Chrome, dragging feature may activate "split view" tab. I recommend using Microsoft Edge instead.

If you need help to find any specific cards, use the chooser(the containers) as following :

You can click on a symbol(letter) in the symbol container to highlight the cards that contains the chosen symbol and click on two symbols to highlight the card that contains both of those symbols.
Similarly, you can click on any card to highlight the symbols that card contains and click on two cards to highlight the symbol that the both of those cards contains. (Hint: you can click on the cards after you drag it into the black slots too!)

If the three cards on a line has a common symbol, the symbol will be shown next to the line to verify you have chosen the right cards to form the line, indicating that you are in the right path.

If you think you have chosen a wrong card, you can replace it with another card on top of the "wrong card" or start again using the "Start Again" button.

Happy Dobble-Pappus playing!