Roman numerals and other number systems

I recently created a worksheet generator for Roman numerals. Feel free to use it.

Roman numerals is not any major topic in the math curriculum. They are still used in clocks, to number chapters of a book, write year numbers, and such, so students need to study them, even if just briefly. Fortunately it isn't that difficult a topic.

Many youngsters might, in fact, be interested in learning about different number systems that have been used in various civilizations over the centuries.

I just posted about writing in math class, and this topic would make for an excellent writing project that connects math, writing, and history. Then you wouldn't be doing it just for the sake of learning the math, or the historical facts, but also to practice writing a report or an essay.

It's probably the easiest to work into the curriculum if you're homeschooling, because classroom teachers may have to just kind of scurry by the Roman numerals on into the next topic. But even if you're a teacher, consider printing out a few interesting articles about the various number systems, such as the Mayan, the Egyptian, or the Babylonian, and then giving these printed articles as extra reading to kids who might be interested in such.

Ideas for a writing project on number systems

1. A report on Mayan, Babylonian, Egyptian, or Chinese numbers. Even younger students could probably write a few sentences and give a few examples of their numbers. You can easily find articles to print about them on the Internet. Wikipedia is a good starting point.



2. Another writing idea is to study several number systems at once, and write a "comparison report" where you compare these other systems to our current number system, which is called the Indian-Arabic number system.
   
   Some main points for such comparison are:
   
   * How many symbols are used?
   * Are they used additively? Or is it a positional system?
   Or a mixture of both?
   * What are the bases used? (could be 10, 20, 60)
   * How easy is it to perform the basic four operations?



3. Yet a third way is to write a report about base 2 numeral system and systems with other bases. This would work best with middle and high schoolers, and should appeal to any computer science minded folks, BTW, because computers use base 2 in their "internal workings".

---

Some resources

Use these web sites to get you started.

Roman Matching Game
Drag the Roman numerals to the corresponding Arabic numerals. If you win the next game will be faster. See if you can beat the clock!

Roman Numerals - Wikipedia
An article explaining the usage, origin, and a chart of Roman numerals.


Numbers
A comprehensive website about various number systems, such as the Egyptian, Babylonian, Chinese, Greek, Roman, Mayan, and Arabic.

Numeral Systems - Wikipedia
Wikipedia article on numeral systems, which contains links to Hindu-Arabic systems, Asian numerals, Alphabetic numerals such as Greek or Hebrew, and other systems including Mayan, Roman, and Babylonian.

Mayan Mathematics

Roman numerals and other number systems

I recently created a worksheet generator for Roman numerals. Feel free to use it.

Roman numerals is not any major topic in the math curriculum. They are still used in clocks, to number chapters of a book, write year numbers, and such, so students need to study them, even if just briefly. Fortunately it isn't that difficult a topic.

Many youngsters might, in fact, be interested in learning about different number systems that have been used in various civilizations over the centuries.

I just posted about writing in math class, and this topic would make for an excellent writing project that connects math, writing, and history. Then you wouldn't be doing it just for the sake of learning the math, or the historical facts, but also to practice writing a report or an essay.

It's probably the easiest to work into the curriculum if you're homeschooling, because classroom teachers may have to just kind of scurry by the Roman numerals on into the next topic. But even if you're a teacher, consider printing out a few interesting articles about the various number systems, such as the Mayan, the Egyptian, or the Babylonian, and then giving these printed articles as extra reading to kids who might be interested in such.

Ideas for a writing project on number systems

1. A report on Mayan, Babylonian, Egyptian, or Chinese numbers. Even younger students could probably write a few sentences and give a few examples of their numbers. You can easily find articles to print about them on the Internet. Wikipedia is a good starting point.



2. Another writing idea is to study several number systems at once, and write a "comparison report" where you compare these other systems to our current number system, which is called the Indian-Arabic number system.
   
   Some main points for such comparison are:
   
   * How many symbols are used?
   * Are they used additively? Or is it a positional system?
   Or a mixture of both?
   * What are the bases used? (could be 10, 20, 60)
   * How easy is it to perform the basic four operations?



3. Yet a third way is to write a report about base 2 numeral system and systems with other bases. This would work best with middle and high schoolers, and should appeal to any computer science minded folks, BTW, because computers use base 2 in their "internal workings".

---

Some resources

Use these web sites to get you started.

Roman Matching Game
Drag the Roman numerals to the corresponding Arabic numerals. If you win the next game will be faster. See if you can beat the clock!

Roman Numerals - Wikipedia
An article explaining the usage, origin, and a chart of Roman numerals.


Numbers
A comprehensive website about various number systems, such as the Egyptian, Babylonian, Chinese, Greek, Roman, Mayan, and Arabic.

Numeral Systems - Wikipedia
Wikipedia article on numeral systems, which contains links to Hindu-Arabic systems, Asian numerals, Alphabetic numerals such as Greek or Hebrew, and other systems including Mayan, Roman, and Babylonian.

Mayan Mathematics

Archimedes knew more than we thought

This story is fascinating; they found a long-lost works of Archimedes under the text of a prayer book, and used modern technology to "see" under the prayer text.

After the text was recovered, it was discovered that Archimedes actually found some of the principles of calculus, and used them to figure out volumes and areas. He dealt with "actual" and "potential" infinity, which is exactly what calculus is about.

And he lived thousands of years before Newton!

A long-lost text by the ancient Greek mathematician shows that he had begun to discover the principles of calculus.

Archimedes knew more than we thought

This story is fascinating; they found a long-lost works of Archimedes under the text of a prayer book, and used modern technology to "see" under the prayer text.

After the text was recovered, it was discovered that Archimedes actually found some of the principles of calculus, and used them to figure out volumes and areas. He dealt with "actual" and "potential" infinity, which is exactly what calculus is about.

And he lived thousands of years before Newton!

A long-lost text by the ancient Greek mathematician shows that he had begun to discover the principles of calculus.

Humorous short history of mathematics

Enjoy:

A Very Short History of Mathematics

This is how it starts:

MATHEMATICS is very much older than History, which begins* in +1066, as is well known; for the first mathematician of any note was a Greek named Zeno, who was born in -494, just 1,559 years earlier. Zeno is memorable for proving three theorems: (i) that motion is impossible; (ii) that Achilles can never catch the tortoise (he failed to notice that this follows from his first theorem); and (iii) that half the time may be equal to double the time. This was not considered a very good start by the other Greeks, so they turned their attention to Geometry.

continue here...

Hat Tip to Let's Play Math.

Humorous short history of mathematics

Enjoy:

A Very Short History of Mathematics

This is how it starts:

MATHEMATICS is very much older than History, which begins* in +1066, as is well known; for the first mathematician of any note was a Greek named Zeno, who was born in -494, just 1,559 years earlier. Zeno is memorable for proving three theorems: (i) that motion is impossible; (ii) that Achilles can never catch the tortoise (he failed to notice that this follows from his first theorem); and (iii) that half the time may be equal to double the time. This was not considered a very good start by the other Greeks, so they turned their attention to Geometry.

continue here...

Hat Tip to Let's Play Math.

Mathematics: The science of patterns

I just started reading the book Mathematics : The Science of Patterns by Keith Devlin. I'm planning on writing a review of it for my site. I can already tell it's a good book, and I've just read the prologue, titled "What is mathematics?"

The author says that yes, mathematics WAS the study of number - up till about 500 B.C. Then it became the study of number and shape. After invention of calculus, it became the study of number, shape, motion, change and space.

But nowadays you can't say that any more, because the field of mathematics has expanded SO much: in 1900 it would have taken about eighty books to write all the world's mathematical knowledge. Devlin estimates that nowadays (or when he wrote the book about 10 years ago) it would take maybe 100,000 volumes to contain all knonw mathematics!

You know, your average person doesn't realize that. I got a glimpse of it while in university, when I saw all these lists of subcategories of mathematics, and when I studied a little bit of something like Abstract Algebra or Complex Analysis or Measure Theory - and all we did was touch the surface of such topics.

And so today, mathematics is often defined as the study of patterns - numerical patterns, patterns of shape, patterns of motion, and so on.

Devlin also touched on beauty in mathematics in his prologue - and I agree: mathematics is beautiful. That, too, I fear, most folks don't realize or understand. It's because you need to be able to understand the math first - then it kind of forms a picture in your mind of a structure that is beautiful, harmonious. I can't explain it.

So I want to recommend the book Mathematics : The Science of Patterns for all of you even before I've written complete review on it. It's written for a layman, and is about the essential history of mathematics.

Categories: philosophy, math

Mathematics: The science of patterns

I just started reading the book Mathematics : The Science of Patterns by Keith Devlin. I'm planning on writing a review of it for my site. I can already tell it's a good book, and I've just read the prologue, titled "What is mathematics?"

The author says that yes, mathematics WAS the study of number - up till about 500 B.C. Then it became the study of number and shape. After invention of calculus, it became the study of number, shape, motion, change and space.

But nowadays you can't say that any more, because the field of mathematics has expanded SO much: in 1900 it would have taken about eighty books to write all the world's mathematical knowledge. Devlin estimates that nowadays (or when he wrote the book about 10 years ago) it would take maybe 100,000 volumes to contain all knonw mathematics!

You know, your average person doesn't realize that. I got a glimpse of it while in university, when I saw all these lists of subcategories of mathematics, and when I studied a little bit of something like Abstract Algebra or Complex Analysis or Measure Theory - and all we did was touch the surface of such topics.

And so today, mathematics is often defined as the study of patterns - numerical patterns, patterns of shape, patterns of motion, and so on.

Devlin also touched on beauty in mathematics in his prologue - and I agree: mathematics is beautiful. That, too, I fear, most folks don't realize or understand. It's because you need to be able to understand the math first - then it kind of forms a picture in your mind of a structure that is beautiful, harmonious. I can't explain it.

So I want to recommend the book Mathematics : The Science of Patterns for all of you even before I've written complete review on it. It's written for a layman, and is about the essential history of mathematics.

Categories: philosophy, math