Category Archives: Math Blunders

How to lie with your graphs

Stumbled across an interesting little post about 5 ways that you can lie with your graphs.  Actually, a better lesson to take from the post is “5 ways other people lie with their graphs and now you can call them on it.”

The post was on Talking Squid, entitled “Five Easy Lies”: Two of the most common ones I’ve seen in talks are below:

  • Choose your cutoffs
    image 
  • “The trend shows no increase for the last [n] days/months/years.”

    Don’t mention the previous [20 n] data points.

  • Talk about the trend of the trend
    image
  • “Sure the graph is going up for now, but the rate of increase is going down.”

    If this fails, talk about the rate of increase of the rate of increase. Keep on differentiating until you find a curve that matches your needs. If all else fails, try logarithms.

Read the rest…

The last comment reminds me of Mar’s Law that stumbled upon a couple of days ago:

Everything is linear if plotted log-log with a fat magic marker.

Why would I even need to learn that?

I have a calculator.  I can answer all the math problems I’ll ever need because I own a calculator.  There are many people that worry me when they say they were never any good at math: the nurse administering the medication, the clerk counting my change, the broker managing my investments, the salesman offering me financing at the car dealership, and now, the cop giving parking tickets:

From 360 (Unofficial Blog of the Nazareth College Math Department in Rochester, New York):

The Herald reported last week that a Traffic Warden was incorrectly ticketing cars in a Devon, England parking lot because of how he was using a calculator. In this parking lot, drivers would pay for a certain amount of time and then post a slip in the windshield with the time they’d entered and how long they’d paid for. One driver, for example, entered at 2:49pm and paid for 75 minutes.

Now 75 minutes is 1 hour, 15 minutes so the driver was covered until 4:04pm. But the Traffic Warden figured out the expiration time by entering in 14.49 into his calculator (for 1449 military time, which corresponds to 2:49pm) and adding on 0.75 (for the 75 minutes). He got 15.24, which he interpreted as meaning that the driver was only covered until 3:24pm. Since it was already 3:41pm, he issued the car a ticket. The car owner saw all this and tried to explain the error — that hours have 60 minutes, not 100, so standard decimal addition doesn’t apply — but the Traffic Warden didn’t see any problem and continued to ticket cars.

In good news, after appeal the incorrect tickets were repealed and a letter of apology sent.

Fair and Balanced

Did you know that 95% of all statistics reported on blogs are made up?

Not only that, but you have to be particularly careful when reading reports coming out from the media that interpret poll results. Here’s a perfect example.

Two stories came out from the Associated Press in the last two days. The first story was out on December 30,
AP Poll: Americans Optimistic for 2007.

Apparently, this was a little too upbeat and positive so the next day they offered this story,
Poll: Americans see gloom, doom in 2007.

Here’s the irony: They’re reporting on the same poll!

HT: Little Green Footballs

Where’s the other dollar?

647617_pizza_calabreza.jpgThree guys in a hotel call room service, place an order for two large pizzas. The delivery boy brings them up with a bill for exactly $30.00. Each guy gives him a $10.00 bill, and he leaves. That’s fact! When he hands the $30.00 to the cashier, he is told a mistake was made. The bill was only $25.00, not $30.00. The cashier gives the delivery boy five $1.00 bills and tells him to take it back to the 3 guys who ordered the pizza. That’s fact! On the way to their room, the delivery boy has a thought…these guys did not give him a tip. He figures that since there is no way to split $5.00 evenly three ways anyhow, he wil keep two dollars for a tip, and just give them back three dollars. So far so good! He knocks on the door and one fellow answers. He explains there was a mix up in the bill, and hands the guy the three dollars, then departs with his two-dollar tip in his pocket. Now the fun begins! Remember! $30-$25=$5. Right? $5-$3=$2. Right? All is well, right?

Not quite. Answer this: Each of the three guys originally gave $10.00 each. They each got back $1.00 in change. That means they paid $9.00 each, which multiplied by three is $27.00. The delivery boy kept $2.00 for a tip. $27.00 plus $2.00 equals $29.00.

Where is the other dollar?

Continue reading

Boycott Pizza Hut! (Updated)

UPDATE: (4:54pm, November 6, 2006) Here’s the letter I sent: Letter to Pizza Hut.pdf

PizzaHutt.jpgNo, I am not really calling for a boycott of Pizza Hut, but it was an eye catching title, wasn’t it? My family went to eat at Pizza Hut today and while we were waiting for my favorite pizza (thin and crispy, meat lovers), Emily and I were playing Tic-Tac-Toe on their kid’s placement. I do appreciate restaurants that provide a means to keep the kids preoccupied until the meal gets to the table. However, just across the page was a series of “Teasers”, one of which read

Inside a gum ball machine with red, yellow and blue gum balls, all but four are red and all but four are blue. How many gum balls are in the machine all together?

Being Saturday and having turned my brain off for a little R & R, it took me a little while to determine the fact that the question is not well-defined. After determining my solution set, I turned the placemat upside down and was disappointed to read their answer. It read,

Six (two red, two blue, two yellow)

So what’s wrong with that?

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Absent minded professor

halfahead.jpg

I didn’t think I fit into the typical category of an absent minded professor. Perhaps those that know me will disagree. However, today, I proved myself wrong. I realized just a few minutes ago that I taught my entire Intermediate Algebra class with my sweater vest on inside out.

I blame it on Christopher Columbus! (Emily is out from school today, so I didn’t have to get up as early, so I overslept and rushed out the door this morning)

Mathematical Blunder #5

Vector products are non-associative. Apparently a neuron misfired as I wrote out the properties for the cross product of two vectors. Fortunately, one student was on their toes and asked, “Are there more properties than are in the textbook?” To be honest, there are but the one of the ones I happened to list was not. Nevertheless, board blunders are gateways to great explorations. I had fun demonstrating the concepts with two long sticks, a stack of dry erase markers and my thumbs.

By the way, to my wife who researched the usefulness of technology in math instruction, that is a key place where technology does improve math instruction. Don’t you think a computer visual in 3d would be more effective than my thumbs? It seems like my training in OpenGL (3d computer visualization toolkit) would come in handy just for this.

Mathematical Blunder #4

Maybe this is not a true mathematical blunder but I still left the whole situation a little embarrassed. Over New Year’s, I started playing with a “Rubik’s Cube” variant at the in-law’s. It’s apparently called Square 1 or Cube 21.

As has always been my approach with such puzzles, I began by just make small adjustments to determine some of the patterns that I could come up with, each time reversing what I had done, so as to leave it in pristine condition. What happened next kind of reminds me of the old Simple Simon game: the one with the lights that you have to keep mimicking in a longer and longer pattern, which by the way you can play here: Simple Simon.

Anyways, I went too far and could not remember my pattern and was unable to reverse it. From that point on, it was downhill fast. First, I couldn’t get the colors in the right place but was still able to return it to a cube. Before long, there was no hope of returning it even to the right shape. Did I mention that it wasn’t even mine? It belonged to the in-laws and we were about to leave shortly after, so I had to leave it in the most wretched of conditions hoping that they could repair the damage. Just so you know, I tried to blame the two year old but no one bought it.

I received a forward just today with some tips in case you ever get yourself in that situation with a square 1.: (Back to) Square One / Cube 21. I hope they worked. To the victims of my blunder, I’m sorry.

Mathematical Blunder #3

Think numbers not dots!

Problem: (from eon)

A simple little puzzle. Suppose you are given two ordinary 6 sided dice. Is it possible to put the numbers 0-9 (with repetition) onto the faces of both dice, such that using both dice you can display all the days of the month i.e. 01 – 31 .

My Response:

Cant be done.

My reasoning is as follows. Each of the dice must have a 1 and 2, in order to denote 11 and 22. This leave 4 spaces on each die, which in order to denote 01 – 09, we must put a 0 on each of the dice. This leaves 3 space on each die, which if we only but the remaining numbers 4 – 9 (7 total), will not fit in the remaining six places.

Is there a more elegant proof?

I am wrong. It can be done. So can anyone figure out why I am wrong? No cheating by checking out the response by tpc.

Mathematical Blunder #2

The title of this blog seems to imply that this is the second in a series of blogging my mathematical blunders and in a way it is. The first blunder went untitled as such and I am almost afraid to bring attention to it again but was placed in the entry, “I should be fired!”. As I have pondered the content of this blog, I have decided that Monday is Blunder Day. (Yeah, I know it’s Tuesday, but I was sick yesterday, boohoo). It just seems appropriate that the hardest day to get through with out making dumb mistakes at the board should be a day honored by blogging about the careless errors I have made over the last week. The hope is that by doing so, I identify where my tend to make most of my mistakes and rectify that problem. I had in mind the blogging of some great ones, but realized that most of the mistakes I make are rather uninteresting. So, lucky for you, I decided to blog them anyway.

“So, ” you ask, “what was the most significant blunder of the week?” In preparing a Calculus Exam over Infinite Series and Sequences, I had given a review sheet to the class explaining that the test would be made up of very similar questions to the review. So on the review, one of the questions was simple enough:

a. Find the Taylor series expansion for [tex]f(x)=\ln (x)[/tex] centered at 2.

Thus, in quickly revising for the test I made simple change by switching to another innocent looking function, not thinking I’d changed the problem significantly.

a. Find the Taylor series expansion for [tex]f(x)= \sin(x^2)[/tex] centered at 2.

It’s the centered at two that is ugly. Now for the math majors or mathematicians out there that read this. Let me ask you to do this. Find the answer and write it in a general summation form. Then tell me how long it took you to discover the pattern needed to write the general formula for the nth term of the series. Then answer me this: Was I unreasonable to make this one of 10 problems for an hour and 15 minute exam?

For you non-mathematicians, you may remember me as the cruel beast of a teacher how discovers the difficulty of his tests only after he “inflicts” them upon his students. Wah ha ha ha ha! (evil laugh)