I remember doing this a long time ago in school and being frustrated by it. Turned out that we did it correctly but we couldn't see it by looking at it directly - we had to use peripheral vision. You could try that, or try taking a long exposure photograph if possible.
Here's a few guesses
- It was an aesthetic or stylistic choice not to have or want paintings to be as realistic as sculpture
- Surprising as it may seem since the ray model of light was understood, maybe no one had yet applied it to artwork. Heck, it wasn't until Brunelleschi published his book...
Three options to consider:
1) Simply evaluate your function using measurements that result in the highest and lowest possible values, in this case calculate area given by the maximum probable measurements and the minimum probable measurements. The difference in these values will be roughly...
@Martyn Arthur, if you can find access to, or purchase for yourself, the book Physics, The Human Adventure by Horton and Brush you'll find a nice discussion of Newton's synthesis of Kepler's laws that uses only algebra (but only addresses circular orbits) in Chapter 11. Further, the discussion...
Instruments and vocals are recorded to different tracks that can be panned left or right. Sometimes the pan is subtle and other times it can be panned completely to one side, or even changed to give a sort of 'dizzying' effect.
Well the ephemerides (had to look up that plural!) that I've looked at don't include quadrature which was surprising. I don't think I'm going to spend money to get data for this one assignment, but I did find a Stellarium script that can toggle this information. For anyone that this may help...
Hi everyone,
I'm looking for a database of planetary events similar to this resource but that has a longer span of time that can be accessed (the site goes back to 2009). I haven't had success in my google searches. Does anybody know where I can find this information?
In particular I am...
I had the J&J about six months ago and it gave me what felt like a slight overnight fever (I woke up but I didn't get out of bed to measure it). No fever in the morning, but I felt fatigued with some mild body aches the next day and I had a very tender arm at the injection site for roughly a...
This is great. Thank you. I've downloaded it and added it to my folder that contains all of my notes from studying these early works (which includes the works of Archimedes). I'm looking forward to reviewing it.
I had a vague recollection of reading about that and I figured that if I mentioned it you'd be able to confirm for me if it was in Hartshorn or elsewhere. Thanks!
Yes, if supplemented I think that could work. I agree with you that seeing a (typically) algebraic representation in a geometric way can offer insight and the example you described above is one of the ones that our small department has shared with students.
Useful? I suppose that depends on...
That comment was driven mostly by the opinion you expressed here:
Which I took to mean that Euclid should be the primary text for HS geometry.
By 'intuition for geometry' I meant the ability to take separate simple facts and use them to develop a proof (i.e. to do what Euclid does). I think...
My impression is that the Common Core is pretty widely adopted. I like the Common Core in principle. In reality there is too much to learn everything well and, because I see students that come from a wide variety of different districts, the things that (I can infer) are omitted from the...
I think elementary school would be too early because algebra I skills are assumed for much of the text. For middle school I think it can be excellent. Our middle school math teacher uses Serra for a geometry course for students who are already comfortable with algebra and I think it has worked...
Here's an online resource that I'd recommend, especially if you're using something like the Green Lion Press version which has no commentary. Navigate to each book by the Roman numerals at the top.
That is a great book.
I'm using Serra's book this year and I like the spirit of it. It is...
But a protractor is a measuring tool, not a construction tool. If we allow measurement then angle trisection is trivial. Interestingly, angle trisection is not possible with a ruler and compass alone.
I'm teaching HS geometry this year and the text we use has a chapter dedicated to...
My college roommate freshmen year was the first seat big band drummer at school and he is the one who introduced me to Buddy Rich. So. Good.
I agree with you about the majority of 'synth-sounding' drum effects. I think my point was just that electronic drums can sound good, but I want drums...
I was going to write a response about Bill Bruford but here's a better source:
https://www.musicradar.com/news/electronic-drumming-pioneers-11-trailblazing-players-who-raised-the-bar-for-electronic-and-hybrid-drumming
Start with Danny Carey (#2). If you like rock music and haven't heard...
An interesting news article.
Part of it describes how starting a treatment (say, opiates for pain) and then substituting placebo afterward (with the patient knowing) can still produce a pain relieving effect. This aligns with an interesting thing I learned from a neuroscientist several years...
If you happen to have access to John R. Taylor's Classical Mechanics there is a chapter dedicated to Chaos near the end. Obviously this will not be very comprehensive (in terms of breadth and depth), but his writing is comprehensive (in terms of accessibility!).
Another accessible text that's...
One entertaining phenomena that could take up a class period or more is to have the students add a couple of drops of food coloring to whole milk on a (clean) plate (thin layer of milk). They can use any color or combination of colors, but it is good to limit them to a few drops. Then, come...
Orbital Mechanics for Engineering Students
Howard Curtis
Appendix D gives several MATLAB algorithms for solving Kepler's equation (all by Newton's method).
Paragraph before the first algorithm:
There is a practical problem with the volume method. The 'crown' was more like a wreath and would not have a substantial enough volume of gold to displace the water significantly enough in the vessel needed to hold the crown (without damaging it) to be confident in the measurments. When...
The original application was for astronomy. There's a book called Heavenly Mathematics which I enjoyed working through recently. It traces the historical development of the math of spherical trig which I found insightful for understanding the formulas you may have seen. One of the...
I can't speak to Germany and Oregon, but here in Vermont the various outbreaks around the state mostly trace back to an outbreak in a hockey league:
https://vtdigger.org/2020/11/30/is-there-a-skater-zero-tied-to-central-vermonts-covid-outbreak/
The recent uptick in deaths stems from outbreaks...
Maybe. Maybe not. I don't think it is unreasonable to look at different time intervals and I can imagine that some folks looked into this without being motivated by partisanship.
Whether or not a person has a partisan motivation behind looking at sub-intervals might be irrelevant if we...
Perhaps part of the problem is that people are considering different time periods. When you look at the data from January there is (currently) no correlation as you point out and all states are doing poorly. If folks want to slice up the time intervals trends may be noticed. For example...
That's a good point. I had overlooked that Goodspeed's charts are only accounting for numbers since July so they tell a different story than if we were counting from January. My mistake.
I understand that. But the overall rates of infection and deaths right now are distributed differently. My point was that, though it may be misleading for news sources to pick individual towns/cities/counties when they say "Hey look at this case/death rate and the fact that they are...
I'm not sure about that. Based on the second source I provided above the top 11 states with fewest cases per million are democratic (one neutral) based on the partisanship metric used, and the top 9 states with most cases per million are republican (one neutral). I'm referring to the most...
Obviously looking at single towns, or perhaps even cities, there are going to be outliers for in either direction from the national trend by political partisanship. But, in the US at this particular time, there seems to be a correlation between political partisanship and both infection and...
An excellent resource is John R. Taylor's An Introduction to Error Analysis. I didn't find it until after I was done with college, but I like the balance he strikes between informality and rigor. There is a short chapter on the method of weighted averages described above.
There's a Fela Kuti song called Equalisation of Trouser and Pant which was the only reason I questioned this statement. Indeed, according to Merriam-Webster 'trouser' is a noun though it is 'usually used in the plural'
Others have already pointed out that this is just a matter of convenience. I'll just add that early trigonometry (and spherical trigonometry) used a radius of 60 (see Ptolemy's Almagest). That was a convention left over from the Babylonian astronomers. I'm not sure when the unit circle was...
I finally had a chance to think about this again after several weeks. I was much more careful in setting up the conditions for the camera but still wasn't able to get results that I trusted. So I bit the bullet and got the app so I could compare the results.
I tried three surfaces: cardboard...
That's a cool idea. I had to go to the hardware store today anyway so I checked out the colorimeter. I used to work in a paint store as a teenager and used one for color matching. I couldn't remember what information was available in the menus, but at this particular store it is limited to...
I agree that for the students that is the important concept. I was asking about the accuracy for my own benefit. But... if there are some simple things that can be done to improve the accuracy and reduce bias in measurements, why not do it?
I don't skip teaching students how to zero a...
Thanks for the thoughts!
As per the saturation issue: on the 0-255 scale that is used how high do you think is too high? I took several photos of paper in direct sunlight and had values for average intensity around 245.
Indeed, I thought of that. Before I got the gray card I tried using a...
Background: This fall our initial plan will have high school students on campus 1 day per week and working remotely for the remainder of the week. I'm trying to plan for some at-home labs and projects. I came across http://albedodreams.info/how_to/how-to-calculate-albedo-yourself/ site which...
There's nothing more convincing than experimental evidence. When I teach this subject I start with a demonstration using "Pascal's apparatus" which shows that the force exerted by a column of liquid with a given base area depends only on the height and not the volume (and thus not the weight)...