coder, writer, thinker, doer. probably not in that order.

Sympose It

Sympose It is a straightforward but very unconventional algebra aide, targeted to those who could use a boost in algebraic intuition. I’ve only developed it for iOS so far, and it’s available on the Apple App Store.

Video Tutorial Watch non-mobile for better video quality.

Text Tutorial Step 1: enter an equation and hit “Go”
Step 2: select the equals (=) in the diagram by tapping it or an inverse (/ or \) by tapping the node behind it
Step 3: tap a highlighted location in the diagram to move the selected equals or inverse there
Step 4: watch the equation change in the bottom textfield; hit “Use” to copy it to the top
Step 5: hit “Recenter” after moving the equals to redraw the equation with the centered equals
Step 6: hit “Help?” to bring you to this page.

Notes
1. You can only make levels by interleaving additive nodes and multiplicative nodes.
2. An exception to #1 is by interleaving additive nodes and multiplicative inverses.
3. When you move the equals through a node to one of the node’s branches, all the other branches get inverses of the same type (color coded) as the node.
4. When you move an inverse through a node of the same type to one of the node’s branches, all the other branches get the same inverse.
5. You can’t move a multiplicative inverse through an additive node (this explains #2).
6. You can move an additive inverse through a multiplicative node, but then nothing happens to the other branches.

Questions
1. Is it possible to construct another operator like addition or multiplication, with its own inversing? (hint: commutativity & associativity, hyperoperation)
2. What else can you think of?

The Central Idea
Equations can be represented as trees, and any portion of the equation can be solved for by re-rooting the tree. As simple as the last half of that idea is, I haven’t seen it before, even after scouring the Internet. So I had to make an app. Let me know if you dig anything up!

Further Work
Equations where the same variable appears more than once cannot be represented by a tree. Instead, their graphs are cyclic. As of now, I’m not interested in implementing this on my own, but I am open to offers from anyone who may be interested, especially those who want to buy the app off of me.