Math Is Fun Forum

Thanks bobbym. My students will also be responsible for a biography of a famous mathematician and a written response to a Numberphile video.

If you have any ideas about possible research questions, I'd love to hear them!

Initially I thought this hint was unhelpful, but it turns out it was just what I needed. My solution:

This took some manipulation and creative thinking. I'm wondering: is there a method that yields the solution without requiring creativity?

This is great, thank you. I look forward to part 2.

A few months ago I wrote a random Haiku generator in Python. Here are some that it wrote:

A hungry baby
wonderfully but poorly cries
over bright crayons

The cute, little spring
eagerly but sadly walks
through cool, bouncy stars

The happy puppy
poorly, not loudly, kisses
for fractal muffins

The dumb, hungry sky
angrily and sadly thinks
about green lettuce

They're nonsensical, but I think they are funny. I hope you like them.

Round 2:

149 = ∫|2x|dx  (-7<x<10)
148 = 37*2^(∑2^-i)  (0≤i<∞)
147= 12110 (base 3)
146 = 100 + 50sin(x) + 4sin(3x)  [x=pi/2]
145 = curve length from 0 to arcsec(46) of ln(cos(x))
144 = Only square Fibonacci Number > 1
143 = CXLIII (roman numerals)
142 = ∑(5+n²)²  [0≤n≤2]
141 = ∑(2-|n-1|²)10^n  [0≤n≤3]
140 = x²(x+3)(4x+1)  [x=2]
139 = 2n+1  [n=integral from 0 to 3 of 23 dx]
138 = f'(6)  [f(x) = (2/3)x³ +4x² +18x + 7]
137 = distance between (12,-5) and (100,100)
136 = zz*   [z = 10+6i]  [z* is the conjugate of z]
135 = 5x^x [x=3]
134 = 10n + ((n+1)(n-1)+1)/n -2cos(π)
133 = ∑11^n  (0≤n≤2)
132 = 10^2 + 2^5
131 = (120x +11x -100 -31)(x+1)/(x^2-1)
130 = 104% of 125
129 = distance between (0,0,0) and (4,7,8)
128 = 2^n  [n = lim (n -> 1) (7x-7)/(x-1)
127 = cuberoot(x-2)=5  [solve for x]
126 = exp(ln(2) + 2ln(3) + ln(7))  [exp(x) = e^x]
125 = (n+1)^(n-1)  [n=4]
124 = Surface area of a rectangular prism with side lengths 2, 4 and 9
123 = ∑(3-n)10^n  [0≤n≤3]
122 = |11+i|²
121 = f(6)   [f(n) = 3*f(n-1)+1, f(0)=1]
120 = Cent et vingt
119 = a^b-(a+b)  [a=2, b=7]
118 = 6!/5 - 62
117 = ∑(3n)²  [2≤n≤3]
116 = (-3+3√(3)i)³-100
115 = max(228x-x²)
114 = a^b-(a*b)  [a=2, b=7]
113 = x² = 15² + (x-1)²  [solve for x]
112 = ∑2^n  [4≤n≤6]
111 = 11² - 10
110 = [see below]
109 = |60+91i|
108 = (a^a)(b^b)  [ab = 6 = a+b+1]
107 = 3 + 54 + 31 + 19
106 = zz*  [z = 5+9i]
105 = Product of first three odd primes
104 = exp(3ln(2))*exp(ln(13))
103 = Sum the roots of x² - 103x + 2652]
102 = curve length from 1 to .25(205 + sqrt(42033)) of x²/2 - ln(2x)/2
101 = ∑ n!*(-1)^(n-1)  [1≤n≤5]
100 = ∑ 2n+1  [0≤n≤9]

If any others need to be LaTexed let me know. It's so tedious I tried to do with out it...

What is your target demographic for this? Are you a teacher? If so, what age group are your students? If you are in fact a teacher, I'd suggest having your students do the rest (numbers 1 through 99). There's a lot more to be gained from creating these formulas than there is to solving them.

I think I'm going to pass on the remaining 99, I've been spending too much of my time on this. If you really want me to them, I will, but as I said... they're super educational (and tons of fun).

Of course. I think "intelligence" is an emergent phenomenon. I don't think a program (or organism) is truly intelligent unless it can learn and I think emotions are a side effect to learning. To the best of my knowledge (which is very, very limited) there are two approaches to AI: the "top down" approach and the "bottom up" approach.

The top down approach is simply programming a computer to be knowledgeable. A program knows something because it is programmed to know something. An example of this I made is here: http://spamtheweb.com/ul/upload/140410/77502_face.php. This is a very simple program that will tell you if a mouse drawn face is smiling or frowning. Try it out by drawing a "smiley face" and then pressing space. How did it know? Simple, when I made it, I told it what a happy face looks like (And what a sad face looks like). This program may give the impression of intelligence, but (as far as I'm concerned) it's not.

The bottom up approach is to program a computer with very simple rules and have the program "learn" over time. Here the program is born stupid but it not stagnant. (I don't have a good example to post, sorry). My belief is that any being (organic or artificial) that can learn will develop emotions. To me, thinking and feeling are the same thing. As far as I'm concerned, the brain is simply a computer and any computer built to be as intelligent as a human brain is probably going to have many of the tendencies. Sufficiently intelligent computers will make mistakes, feel emotions and even behave irrationally.

Two books I recommend: Artificial Life by Steven Levy (non-fiction) and Galatea 2.2 by Richard Powers (fiction). Both of these books explore this topic extensively.

Calccrypto: I don't understand your question. I use IDLE to write my programs (and more recently PyScriptor). Make no mistake, I have no idea what I'm doing, I'm doing this for fun.

Ricky: Wow, that's a whole bunch of techno-lingo, but at least I have a starting place. Am I going to have to learn Java to use Jython? How do I figure out which implementation of Python I'm using? IF I'm using the wrong implementation of Python, how do I use the right one? And how will that change what I'm doing?