Interactive Midpoint Formula
I hope everyone had a great time over the holidays reconnecting with their family and friends. I definitely enjoyed hearing about the changes in their lives since we last spoke, and meeting new additions to the families. One of the best times I had was with a two year old who I had met earlier in the year. She was much more responsive this time, and as we sat and talked, she was eager to tell me the things she knew, from the alphabet to her numbers, to her shapes. So today’s blogscript is inspired by this conversation, which became a game of point and describe. I would point to an object and she would say “That’s a circle”, or “That’s a red triangle”. I was amazed at both how simple it was and how much I enjoyed this activity.
I enjoyed it so much that I decided that I’d like to have some programs on my site that were more of this genre. The first that I decided to write is a lesson on the midpoint formula. But instead of simply giving the formula and writing a script to walk users through the steps in calculating the midpoint, I thought I’d write a pointandclick approach to it.
The script will randomly generate two points in the XY plane and ask users to calculate the midpoint between these points. Five options are then given and the user is asked to select the radio button next to the correct choice. Once the submit button is pressed, the program will let users know if their choice is correct. Users can have the program generate new points at any time. There is also an option for users to have the midpoint formula displayed.
Because this is my first program of this sort, I am curious to know what users think. When generating choices that are supposed to be incorrect, what’s a good method for doing so? I decided not to keep a timer or a score for the “score” of a user, but I did think about it. Ultimately I wanted this to feel less like a “test” and more like a “game” so I decided against this option. But I would like to know what you think – either through your comments here or on twitter @MindAfterMath.
Once again, here’s the link to the script. I’ll keep you updated on if my new two year old friend likes this.
Triangle Sum Puzzle
The Bridge Crossing Problem
 Each person has a travel time across the bridge.
 No more than two people can cross the bridge at one time.
 If two people are on the bridge together, they must travel at the pace of the slower person.
 There is only one flashlight and no party (of one or two people) can travel across the bridge without the flashlight.
 The flashlight cannot be thrown across the bridge, and nobody can go to the store to purchase another flashlight
Magical Squares Game
8  3  4 
1  5  9 
6  2  7 
4  1  16  13 
15  11  2  6 
10  14  7  3 
5  8  9  12 
QR Decomposition
and
e_{k} = u_{k} / u_{k}
Then Q = [e_{1}, …, e_{n}] and
R = 

The A* Algorithm
Naive Bayesian Classification
P(C  F_{1}, …, F_{fn}) = 
 
= P(C) P(F_{1}  C) * … * P(F_{fn}  C 
 
= P(C) _{i = 1 to nf}P(F_{i}  C) 

Hierarchical Clustering
 KMeans Clustering requires an initial number of desired clusters, while Hierarchical clustering does not.
 A run of KMeans Clustering will always give K clusters, whereas Hierarchical Clustering can give more or less, depending on our tolerance .
 KMeans can undo previous mistakes (assignments of an element to the wrong cluster), while Hierarchical Clustering cannot.