Comment due Sunday, November 17
Option 1
Pi day is usually celebrated by eating pie on March 14, since $\pi$ is approximately 3.14.
While $\pi$ is a familiar constant to most math students, the constant $e$ is less well known. Some of you are seeing the constant $e$ for the first time in this class! We use the notation $e$ to represent an irrational number whose value is approximately 2.718.
There are different ways of defining $e$ but most of them are not geometric. (Compare this to $\pi$, which can be defined as the ratio of the circumference of a circle to its diameter.) The number $e$ appears naturally in contexts involving change, which is why you’ll see it again in your calculus class.
For this activity, you will watch one of the videos linked below (or another video of your choosing) which each describe where $e$ comes from together with some of its properties (there are lots of videos about $e$ because it has lots of properties!).
After you watch the video, comment on this post with a short summary of it. Be sure to include:
- which video you watched,
- one thing that you learned about $e$, and
- a question you still have about $e$ (something you’re curious about).
Videos
- e (Euler’s Number) – Numberphile
- Transcendental Numbers – Numberphile
- Euler’s Formula – Numberphile
- A proof that e is irrational – Numberphile
BTW, Numberphile is a really fun YouTube account where they ask experts to talk about incredible math facts, so you might like to check out their other videos. The videos linked above are at varying degrees of difficulty, so don’t worry about trying to understand absolutely everything. Just try to find one thing that you learned. If you watch a video on $e$ other than the ones liked above, include the link to the video you watched in your comment
Option 2
You may have felt the earthquake that our area experienced back in the spring, or maybe some of its smaller aftershocks. The epicenter of the first earthquake was in New Jersey and it registered at 4.8 on the Richter scale. You may have heard that the Richter scale is logarithmic, but what does that mean? Choose one of these videos to watch for an explanation of the Richter scale:
- Richter scale | Logarithms | Algebra II | Khan Academy (this video is a bit old, so the east coast one it’s referencing isn’t the one we just experienced, but one from back in 2011)
- The Connection Between Mathematics And Earthquakes Using Logarithms (this video was recorded after the recent 7.4 earthquake in Taiwan, but before our recent 4.8 earthquake)
In the comments below, include:
- which video you watched,
- one thing that you learned about the Richter scale, and
- a question you still have about earthquakes (something you’re curious about).
Option #1 e(Euler number) – Numberphile
In the video, Numberphile explains the complexity of the number e and what makes it stand out from the rest. Where in the video it explains that the number e is a repeating decimal similar to PI (3.141…..), implying that the number e is an irrational number. In the video, I learned that “e” is not based on a shape or any form of geometry but instead its a mathematical constant that is based on rate of change, meaning e is mainly used in exponential growth/decay. My question is can the number e be used for something other than exponential growth/decay?
Option 2 (Richter scale)
I think ,the Richter scale is a logarithmic scale that measures the energy release of earthquakes. I just want to know how much bigger one earthquake is compared to another
1.The video about Euler’s number by Numberphile is about how e is used in the mathematics world. e is an irrational number that is related to growth and the rate of change. Euler created a formula for e that has a pattern and goes up to the 18th decimal. He also found the value of e by using factorials. Something I found interesting is that e is the only formula that has a value gradient and area at every point in a line. Something I questioned was e able to be related to logarithms or In?