- Here's a video covering the material today.
- You have an IMath assignment, which will be due soon.
- I've also added a new assignment; pay attention to your schedule -- here, NOT ON CANVAS. Remember, Canvas is not your home page; this is. However, you will submit your assignment on Canvas. Canvas is a tool, which we use; but our website is here.
- Last time we looked into two things:
- Your reading: Early Concepts of Number and Counting
- The sieve of Eratosthenes, an ancient (Greek) method for finding prime numbers.
One of the most important things about counting numbers is that they can be factored into a product of prime numbers in a unique way: but it turns out that it's very difficult (and slow) to factor very large counting numbers into primes.
And this odd fact about prime factorization is what's protecting you on the internet. Your hero, prime numbers!
- Today we're going to look into the mathematics of the
Mayans: what were the Mayans doing over in the new world?
- Take a look at this Mayan lunar calendar (from Xultun,
Guatemala -- here's a map):
"The Maya also made their own very accurate measurement of the solar year, putting it at 365.242 days. The latest computations give us the figure of 365.242198: so the Maya were actually far nearer the true figure than the current Western calendar of 365 days (which, with leap years, gives a true average of 365.2425)." From The Universal History of Numbers, by George Ifrah.
- How can we make sense of the numbers that are appearing?
- What are the symbols appearing in their writing?
- What distinguishes the Mayans from the Babylonians?
- Let's do a few examples with Mayan numbers: let's write
- 37 in Mayan
- 694 in Mayan
- 1034 in Mayan
- Here are the answers (with video)
- So the Mayans
- had a base 20 system -- they counted with their fingers and their toes!
- did have one special place when doing solar/calendar
calculations: they changed the third place to 360
(=18*20), which we believe was "in honor" of the number
of days of the year (360).
- liked to group into four groups of fives -- perhaps one
for each appendage's extremeties.
- And rather than building sideways, like the Babylonians,
they built up! Toward the heavens....
- But perhaps the coolest thing about the Mayans was that they had a zero! They knew the value of nothing....
- had a base 20 system -- they counted with their fingers and their toes!
- Take a look at this Mayan lunar calendar (from Xultun,
Guatemala -- here's a map):
- Here's your Mayan writing resource.
- Links:
- In 2016, the largest prime number was $2^{74,207,281}-1$; but it didn't last long: in 2017, the prime $2^{77,232,917}-1$ was discovered, and that's the biggest known to date.
- Maya Decipherment: Ideas on Ancient Maya Writing and Iconography
- Ancient Maya Astronomical Tables from Xultun, Guatemala
- Have We Been Misreading a Crucial Maya Codex for Centuries? A new look at the Dresden Codex may change our understanding of the ways the Maya used the night sky to plan their ceremonial calendars.
Website maintained by Andy Long. Comments appreciated.