Comment due Sunday, April 14
Option 1
We missed pi day! 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 on Friday morning, 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).
The video I watched was the second one about the 7.4 magnitude earthquake in Taiwan. I chose it for its relevancy as it happened more recently. Something I learned about the richter scale is that it measures an earthquakes intensity and the magnitude ranges from 1-10. A question I have about earthquakes is what determines their frequency and how often they may occur.
I watched the first video that was linked about e. And one thing that i learned about e was that it is irrational and also one more thing that i thought was cool was that the creator didn’t name it e because of his name but that it was a complete coincidence. A question is what was Euler’s thought when he first discovered e and what was his reaction to it?
The video I chose was Euler’s number. One thing I learned from the video was he was the first to find out what was the continuous interest which was his number 2.178. My question is what math class would you use Euler’s formula?
I watched Khan Academy’s video on Richter Scale, and learnt that the Richter Scale was developed by Charles Richter. And the scale maxes out around the magnitude 7. My question is; Is there a natural way to prevent earthquakes?
I watched “Math and Seismology. How to find the magnitude of an Earthquake. Richter Scale”. Something I learned about the Richter scale is that Charles Richter discovered the standardized measurement for earthquakes by measuring a small earthquake and discovering that the Log of A sub-zero is -1.7 when 20 meters from the epicenter. A question I still have is what were peoples first reactions to earthquakes.