Origin of Numbers
Please send your completed work to [email protected]. No attachments will be opened. The subject line should read "Magical Numbers- HW1 - HOL Name" and you should include your HOL name and house in the body of the email.
There are more than 60 points worth of options below. You can pick which ones you would like to do, but you cannot earn more than 60 points.
If you include any images in your assignment, please upload them to a site such as Postimage and send me the link.
There are more than 60 points worth of options below. You can pick which ones you would like to do, but you cannot earn more than 60 points.
If you include any images in your assignment, please upload them to a site such as Postimage and send me the link.
True or False (10 points) - If False, please correct the sentence
1. The Arab system originated in the Middle East.
2. The Egyptian system is an positional system.
3. A stylus was used to write the Babylonian numerals.
4. In the Babylonian system, there is no difference between the way 1 and 60 are written.
5. The Romans used the abacus to add sums together.
Short Answers (10 points) - Answer in full sentences
1. What does it mean that a system of numeration is additive?
2. Why can larger numbers be cumbersome to write with an additive system?
3. What are the two symbols used to create numbers called in the Babylonian system?
4. What is the order of Roman numerals if these are meant to be added together?
5. What is the exception to the rule of how Roman numerals are written?
Opinion - Which System of Numeration? (15 points) - Minimum 150 words
You have now been presented with three early systems of numeration. Which did you like best and why? What could have been done to improve it even further?
Invent a System of Numeration (20 points) - Minimum 100 words + Image OR minimum 150 words
Make your own system. Create an image that contains your symbols (numerals) and describe how the system works in at least a hundred words. Is it a positional system or an addative system? Or a hybrid or something else entirely perhaps? Does it follow the decimal system or does it have another 'reset point'?
If you do not want to make an image you can describe what your symbols would look like instead in at least 50 words.
Food for Thought (10 points)
In the Roman numeral system, how would having a symbol for 0 have allowed for negative numbers and why does the absence of one disallow negative numbers? Explain in as many words as are necessary.
Modern Roman Numerals (5 points)
Take a photo of a modern use of Roman numerals.
Number Identification (10 points)
Identify the value of each of the numbers written below
1. The Arab system originated in the Middle East.
2. The Egyptian system is an positional system.
3. A stylus was used to write the Babylonian numerals.
4. In the Babylonian system, there is no difference between the way 1 and 60 are written.
5. The Romans used the abacus to add sums together.
Short Answers (10 points) - Answer in full sentences
1. What does it mean that a system of numeration is additive?
2. Why can larger numbers be cumbersome to write with an additive system?
3. What are the two symbols used to create numbers called in the Babylonian system?
4. What is the order of Roman numerals if these are meant to be added together?
5. What is the exception to the rule of how Roman numerals are written?
Opinion - Which System of Numeration? (15 points) - Minimum 150 words
You have now been presented with three early systems of numeration. Which did you like best and why? What could have been done to improve it even further?
Invent a System of Numeration (20 points) - Minimum 100 words + Image OR minimum 150 words
Make your own system. Create an image that contains your symbols (numerals) and describe how the system works in at least a hundred words. Is it a positional system or an addative system? Or a hybrid or something else entirely perhaps? Does it follow the decimal system or does it have another 'reset point'?
If you do not want to make an image you can describe what your symbols would look like instead in at least 50 words.
Food for Thought (10 points)
In the Roman numeral system, how would having a symbol for 0 have allowed for negative numbers and why does the absence of one disallow negative numbers? Explain in as many words as are necessary.
Modern Roman Numerals (5 points)
Take a photo of a modern use of Roman numerals.
Number Identification (10 points)
Identify the value of each of the numbers written below
An Egyptian Number (5 points)
Write 99999 with the Egyptian numberals.
Writing Babylonian and Roman Numberals (10 points)
For the numbers written in babylonian numerals you may also write out how many hooks and how many nails each number should have and how they should be placed in relation to each other.
1. Write 25 in Babylonian and Roman numerals
2. Write 65 in Babylonian and Roman numerals
3. Write 605 in Babylonian and Roman numerals
4. Write 404 and 606 in Roman numerals
5. Write 144 and 233 in Roman numerals
Write 99999 with the Egyptian numberals.
Writing Babylonian and Roman Numberals (10 points)
For the numbers written in babylonian numerals you may also write out how many hooks and how many nails each number should have and how they should be placed in relation to each other.
1. Write 25 in Babylonian and Roman numerals
2. Write 65 in Babylonian and Roman numerals
3. Write 605 in Babylonian and Roman numerals
4. Write 404 and 606 in Roman numerals
5. Write 144 and 233 in Roman numerals
Reading the Abacus (10 points)
Identify the numbers "written out" on each of the three abacuses below and write the result both in roman numerals and arab numberals (regular numbers).
Identify the numbers "written out" on each of the three abacuses below and write the result both in roman numerals and arab numberals (regular numbers).
Advantages of the Abacus (15 points)
Try calculating CLXVI + LV without writing the numbers out into arabic numberals (Or if you do, write each symbol's value out and keep track of what must be added and what must be subtracted), and without using an abacus. What is the difficulty in calculating this way?
Try doing it with the help of an abacus. What is the advantage of doing it this way? Explain in as many words as are necessary.
You can find an online abacus here if you don't have one.
Try calculating CLXVI + LV without writing the numbers out into arabic numberals (Or if you do, write each symbol's value out and keep track of what must be added and what must be subtracted), and without using an abacus. What is the difficulty in calculating this way?
Try doing it with the help of an abacus. What is the advantage of doing it this way? Explain in as many words as are necessary.
You can find an online abacus here if you don't have one.