Google Translate

I use Google Translate intermittently, mainly to translate back and forth between Indonesian and English. It's easy to forget that the words that I've looked up are stored and can be exported as a CSV file to Google Sheets. From there the words can be copied and pasted elsewhere, as I've done right here using a small sample:

bee	lebah
investigation	penyelidikan
disability	cacat
anonymous	anonim
iodine	yodium
he is trying to create a positive image	dia mencoba menciptakan citra yang positif
suspicious	mencurigakan
image	gambar
treasonable	khianat
cautious	waspada
hypocrite	munafik
dolphin	lumba-lumba
shark	hiu
whale	ikan paus
cause	sebab

Within Google Translate of course you can hear the words pronounced as well which is of course an added bonus.

It's just made me realise how I underutilise the features of this free service. Evil as it is, Google still offers a lot of useful, free stuff. It's also possible to create a series of flashcards from the spreadsheet, using a template from flippity.net. Figure 1 shows the straightforward instructions:

Figure 1

Here is the link to the flashcards that were created. Figure 2 shows a screenshot of the interface:

Figure 2

Desmos Graphing Calculator

I've been familiar with the Desmos Graphing Calculator since October of 2015 but my last saved file was from October 2016. While watching a video from 3Blue1Brown, I was reminded of this resource again because he made use of it when illustrating graphical properties of quadratic functions. It's remarkably easy to use. I watched a series of short YouTube videos about the Desmos Graphing Calculator, just to refresh my memory and then I was away. It's easy to embed a graph into a blog post as I've done below: 

It's all remarkably easy. In this example, I've hidden the graph of the derivative function but used it to create the tangent to the curve at any point. The slider changes the x value of the point where the tangent touches the graph of \(y=x^x\) and the slope of the tangent changes accordingly.

I'm thinking that I could make use of this resource in the daily analysis of my diurnal age. For example, on July 28th 2020 I was 26049 days old. One of the properties of this number is that it is:

... a member of OEIS A064808: the (n+1)st (n+2)-gonal number (here n=37 so we have the 38th 39-gonal number). The formula is a(n) = (n + 1)*(n^2 + 2)/2 and the sequence, up to and including 26049, can be generated from the following SageMath code:

INPUT

L=[]

for n in [0..37]:

    number=(n + 1)*(n^2 + 2)/2

    L.append(number)

print(L)

OUTPUT

[1, 3, 9, 22, 45, 81, 133, 204, 297, 415, 561, 738, 949, 1197, 1485, 1816, 2193, 2619, 3097, 3630, 4221, 4873, 5589, 6372, 7225, 8151, 9153, 10234, 11397, 12645, 13981, 15408, 16929, 18547, 20265, 22086, 24013, 26049]

This relationship can be easily graphed and a corresponding table drawn up as shown in the embedded graph below:

It's not all that useful here as SageMath can easily produce the same output but it's a little different and could prove useful in the future as an aid to representation and analysis. The table is not visible above but looks like this: