Why would you ever post a math puzzle like this without linking to the solution?

It took me a little while, but here’s my solution:

The area of the total triangle is always 32.5 (5*13*0.5).

The area of the red triangle is 12 (3*8*0.5).
The area of the teal triangle is 5 (2*5*0.5).
The area of the yellow shape is 7.
The area of the green shape is 8.

Now we have a problem. 12+5+7+8 is 32. How is it that the overall area becomes 33 when the shapes are rearranged?

The problem is that the puzzle is bogus.

The area changes because the triangles are not congruent. Their angles are slightly off which causes a unit of slip in either direction spread out across the hypotenuse of both triangles.

The proof is in the angles of the smaller triangles versus the angles of the larger ideal triangle. Solving the triangle for it’s angles reveals the problem.

The Red triangle’s angles are 20.56° and 69.44°
The Teal triangle’s angles are 21.8° and 68.2°
All the triangle’s angles should be 21.04° and 68.96°
(all numbers rounded for clarity)

Another clue is that the leftover rectangular area defined by the two triangles is originally 3*5 units for an area of 15. When the triangles are rearranged, the area becomes 2*8 units, an area of 16.

If the ‘puzzle’ was legit, the red triangle would be 8*3.077 with an area of 12.31 and the teal triangle would be 5*1.92 with an area of 4.81. The magic and certainty of numbers prevail, I hate these kinds of carnival tricks.

My sophomore year of high school I received a “D” grade in Pre-Algebra. I was bored.

These automated triangle solving tools made this go much faster. Here is an MySQL query which returns the angles of the bogus triangles:

SELECT 
ATAN(5/13) * (180/PI()) AS whole_triangle_A,
90 - ATAN(5/13) * (180/PI()) AS whole_triangle_B, 
ATAN(3/8) * (180/PI()) as red_triangle_A, 
90 -ATAN(3/8) * (180/PI()) as red_triangle_B, 
ATAN(2/5) * (180/PI()) AS teal_triangle_A,
90-ATAN(2/5) * (180/PI()) AS teal_triangle_B;

(via Making Light)

Something corrupted my mail preferences this morning. Luckily I didn’t lose anything, partly because of a backup and partly because the application behaved well after crashing. I did lose all my filtering rules, four months of learned junk mail filtering and the record of which messages had already been downloaded from the server. After restoring my prefs and restarting mail, it proceeded to download almost 800 messages, most of which had already been read, responded to and filed. So there went my morning.

If you’re using OS X, back up the Library folder in your Home folder. Just take the whole thing and throw it on a CD if it will fit. Do this regularly. If it wont fit, start by backing up the following folders in your user library:

• Mail
• Application Support
• Preferences
• Keychains (all stored passwords are in here)
• Addresses (all the Address Book stuff)
• Calendars (if you’re using iCal)

Depending on which browser you’re using, these are the locations of their various bookmark files:

Safari: ~/Library/Safari

Chimera: ~/Library/Application Support/Chimera

Explorer: ~/Library/Preferences/Explorer

Phoenix: ~/Library/Phoenix

Mozilla: ~/Library/Mozilla

Opera: ~/Library/Preferences/Opera Preferences

OS X is really good but it’s still a long way from perfect.

JVC Hi-Def camcorder: Like the Panasonic 24fps DVX100, this is going to shake up the DV world all over again. Are Canon and Sony sweating over these? I just hope JVC’s HD format is open and not a repeat of Sony’s almost useless MicroMV format.

My next camcorder will either be Hi-Def or tape-free. Maybe both. And hopefully it will use the Foveon X3 chipset. Lately I’ve been wishing my still camera also shot DV, that would be my dream camera.

I’ve been trying to keep political posts off the site recently, but there were a few things yesterday I wanted to link to:

The Daniel Pearl Foundation: January 23rd marked the first anniversary of the abduction of Daniel Pearl in Pakistan. A month later he was brutally executed for being Jewish and American.

Venezuela: It seems to be getting worse, although I now understand why the Bush adminstration was so quick to recognize last years’ failed coup.

Lastly, a definition of moral equivalence:

Two men watch an old woman crossing the street. One man pushes the woman in front of an oncoming truck. The other man pushes her to safety.

Both men are guilty of pushing the woman.

Bunch of hits today from the links page of a Yahoo! Group mysteriously titled 132C. It looks like a DV editing group, anyone care to let me know anything else about it? Just curious…

Amazing. Phoenix for OS X seems even faster than Chimera OR Safari. This might be the fastest browser for OS X, and it’s just an experiment, built by Kevin Gerich because he “was curious to see if [he] could cobble one together.” Phoenix is an open source offshoot of Mozilla, designed to be fast, lightweight and cross-platform. I now have four browsers in my Dock.

I’ve switched back to Transmit as my main FTP tool for two reasons:

1. It’s really good.
2. I like reading Steven Frank’s blog. (Steven is one of the authors of Transmit and co-founder of Panic Inc.)