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 centre of perspectivity. Desargues's theorem states that the truth of the first condition is necessary and sufficient for the truth of the second.

Play around with Desargues

Use the following applet produced in GeoGebra to play around with the points on the lines (except the axis of perspectivity line) to see Desargues's theorem in action.

Dobble card trick with Desargues's Theorem

Let's try Desargues's 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 either create the axis of perspectivity or the centre of perspectivity. Drag the cards from the cards containers into the circles(points) on the lines and triangles.

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 the 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 and red slots too!)

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.

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.

Happy Dobble-Desargues playing!