Tag Archives: math

Adventures in Mathematics at the National Mathematics Museum

29 Apr

After a losing hope about the state of mathematics in the world, I was delighted to learn about and visit the National Mathematics Museum (MoMath)in New York City. Located at 11 East 26 Street, it opened to the community in December 2015. It is worth the trip!

From the Pi symbol door handles to the hologram engraved art work, each inch of this museum is filled with interesting sites and many interactive activities! I loved riding a bicycle with square wheels. It was a little hard on the rear! But fun.

We three adults were having as much fun as the children. There are two floors of activities that parents and children can work on together. Some are math and logic problems to solve. Others are just fun activities like watching your arms branch out into fractals in a living tree exhibit.

I wish I can tell you my favorite activity, but I cannot since so much of it was great fun.

There is also a room where temporary exhibits are housed. When we were there it was unbelievable math art that has to be made through 3-D printers. And fantastic origami art.

The gift shop is packed with educational games and activities to buy. More important this museum is open every day except for Thanksgiving! Need something to do with your children school age and older, go here! There are events and activities listed on its website which I put below.

It is an easy walk to Madison Garden Park where you can sit for a bit and people watch, take great photos of the flatiron building and buy lunch or a snack.

Being there gave me hope. There are parents and children and grandparents interested math and learning. I did not see one frown while there, I just saw adults and children intrigued by what they were seeing and learning while having an adventure at the MoMath!

Www.momath.org

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Technology Equals No Division

27 Apr

I had the most pleasant dinner with my husband and siblings in a restaurant in Montclair, NJ. The food, fish for all of us and ice cream and sorbet for dessert was delightful. We chatted and ate and visited and finally were ready to leave.

I have to admit that perhaps we asked for too much. We wanted to divide the check so that my husband and I paid half and my siblings each paid a quarter of the bill. The waitress said it was fine. And so we gave her three credit cards and waited. And waited. And waited. I should have known something was not working out.

Our bill for four people was $129.02. She came back with my credit card and a receipt for $86. She then was going to divide the $43.02 between my siblings. I was astounded that she did not even realize that this was not divided in HALF. It was two-thirds and a third, but definitely not half. $86 and $43 are NOT equal!

I went up with my receipts to speak to her while she was running the other cards. I politely said, “Wait. This is not right. $86 Is not half of $129.02.”

She was not convinced. “Are you sure? I have to get my manager,” she told me as she hustled away with a dazed look on her face.

A few minutes later the manager came. “How cam I help? ” He was pleasant.

“This is wrong. $86 is not half of $129.02. ” I told him. I was sure he would understand. But no such luck. “You asked for half on one card and the rest divided between those two!” He told me.

“Yes half. $86 is not half of $129.02. Half of $130 is $65. This is wrong.” I started doing the math, the division on a piece of paper. I showed him the math. But that was not what he needed. I offered to show him on my phone calculator. But no. He had a calculator that he pulled out.

He typed in 1292. No I said. You need a decimal. It is 129.02. He might have been anxious at this point. I noticed my siblings laughing and looking at me. I was getting exasperated. And I now was in teacher mode. I had taught at a high school. There is a definite teacher voice and look that can come over me.

In any case he correctly typed in 129.02 and divided by 2. 64.51 was the number it read. “You are right,” he admitted. “I am sorry. I will fix it. ”

I wanted to make it easy. I wanted him to credit my sister’s account and just put the rest on my card, the other $43.02. We would sort it out later. But that was too much as well. He ended up crediting my account and my sister’s. He ran a new receipt putting all the money on mine. I paid , added tip and we settled up.

My siblings laughed all the way to the car. They knew I was frustrated, they told me that the look of our mother came over me as I tried to explain the math to the manager. Mom taught fourth grade for 30 years.

“I just can’t understand how the waitress and the manager did not see that $86 was not half. $43 and $86 are not equal. Did they not understand half, divide by two,” I was still frustrated.

I was concerned that they did not believe my division that I did on paper. They would only believe a calculator. I felt like I was in a science fiction novel that I had read years ago where a boy who could do math in his head was considered a genius because everyone else HAD to use a calculator!

I am worried Technology is destroying the ability to calculate math in our brains.

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Learning Infinity and Beyond Makes Me Insane

2 Aug
A note from Mr. "Mean" Thoens to me in my senior yearbook. We never did agree on infinite numbers.

A note from Mr. “Mean” Thoens to me in my senior yearbook. We never did agree on infinite numbers.

My disdain for infinity and infinite numbers started when I was a senior in high school. My North Bergen High School calculus teacher, Mr. Ray Thoens, (who I called “Mean” Thoens) was teaching us about infinity and the infinite number of points in a line. Okay, I could get that. But then he told us that two lines of unequal lengths would have the same number of infinite points. What!!

I argued with him.

How can a line this long ___________, have the same number of points as a line this long _________________? The lines have a definite beginning and an end. How can they have the same infinite number of points! For my logical mind, one must have more points than the other.

Mr. Thoens and I argued about this all year. Whenever I was upset about something I would just say, “Yes just like those lines and infinite number of points. It just doesn’t make sense.” And I would sometimes add while shaking my head, “that is just wrong.” Other students in my class perhaps agreed with Mr. Thoens, but that did not change my mind.

Senior year, basically the calculus class. I had a lot of hair, but not as much as the boy next to me.

Senior year, basically the calculus class. I had a lot of hair, but not as much as the boy next to me.

Over the years, the long years, since I graduated high school, I still felt that the information about infinity and lines and infinite numbers of points was a crazy thing and just could not be right. But I kept my point of view to myself all these years. I never took another math class (except statistics), so I did not have to worry about these numbers. And even though my husband studied math and physics for the first two years of his college career, infinite numbers just did not come up.

Until now, when my nephew, my sister’s son, came to stay with us for a few days.

My nephew just earned his master’s degree in mathematics from the University of Kansas. He taught calculus to college freshman for the past few years, and he is staying with me before he leaves for Florida to study for his PhD in math at a university there.

And we got into a math debate.

I am not a hundred percent sure how it started, but we got on to the topic of calculus. I could not help myself, I had to tell him about my disdain for infinite numbers and points in lines.

He said something like, “I will explain it to you. Many people have this problem.”

I said, “You are not going to change my mind. It is not right! I have held this view for 40 years!”

He told me that Mr. Thoens, my high school math teacher was right! Can you imagine that! He told me that my high school teacher was probably trying not to use more advanced math language when he tried to exlain it all those years ago. But he, my nephew had explained this to many students, and he could explain it to me.

The diagrams in my nephew and my debate over infinite points in lines of two different lengths.

The diagrams in my nephew and my debate over infinite points in lines of two different lengths.

He started talking about ‘cardinality’ and how to match numbers. He showed me two sets of numbers, one with three dots and one with five. We could agree that these did not match. Then he added two more dots to make them equal sets. And we could agree that they were now equal.

He made graphs and wrote equation-like things. Who cares? When you look at two lines of unequal length it is intuitive and logical to realize that they do not have the same number of infinite points. ( I spoke to my daughter about this, and she totally agreed! So I must be right.)

I showed him two equal lines, A to B. We agreed that they had the same number of infinite points. Then I added a segment that doubled the size of one line to C. And I said, “This line has more points. It is a longer line.”

And he said, “NO!”

What! How can you say no?

He then told me that “The same way of matching is not going to work.”

Of course it will not. You cannot match the same way because they are different lengths.

And then he went into a silly math concept that showed matching using x/2 (x over 2). In this way the numbers in the longer line matched numbers in the shorter line like this: .3 went with .15 and so on. So! Yes you can make pairs of numbers, but there are always other numbers. He agreed and said something like, “But you never actually get to zero so your cardinality is okay as long as you can keep matching.”

Yes, Mr. Thoens had tried that same trick on me when I was 17. It did not work then and it will not work now.

I appreciate my nephew’s passion for math. I hope he has great success and continues to teach and learn. But I am not changing my mind. Two lines of unequal length and size cannot have the same number of infinite points even if both have an infinite number of points.

And do not tell me that an infinite number of points is an infinite number of points.   I know that. But it is something that does not make sense in my mind, and probably will never make sense.

I think I will just go another 40 years believing that learning about infinity and beyond just makes me insane!

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