Wikipedia:Reference desk/Archives/Mathematics/2022 June 28

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June 28

Rubik’s Cube and Wang Tiles

Hi! I wonder if anyone has ever written about the relationship between a Rubik’s Cube and a set of Wang tiles.

Thanks

Duomillia (talk) 03:20, 28 June 2022 (UTC)

People write about imagined relationships between celebrities, but not so much when it comes to mathematical entities. Is there a relationship? I don't see one.  --Lambiam 08:00, 28 June 2022 (UTC)

Easy Graph Question

A grade 10th question surprised me- it asked to plot the graph for 15x-30y+1=0 and 3x-(24/4)y+(1/5)=0 and find if the lines are parallel, coincident, or intersecting. How do you plot this graph with reasonable coordinates? --ExclusiveEditor _{Notify Me!} 13:18, 28 June 2022 (UTC)

Put them in slope-intercept form. See https://en.wikipedia.org/wiki/Linear_equation#Slope%E2%80%93intercept_form_or_Gradient-intercept_form --Modocc (talk) 13:36, 28 June 2022 (UTC)

@Modocc:The problem is that this problem is for junior high school students who are not taught slope-intercept form but just taught methods like elimination, substitution, and then putting some value to x or y and then finding the other variable's value. Also by this method(taught to students), we find coordinates like 1/30 and 1/15 which are not easily plottable on a graph. So thinking on this level we want a simple answer, or if there is an error in the question itself. --ExclusiveEditor _{Notify Me!} 16:14, 28 June 2022 (UTC)

To find the answer, it does not really matter what the coordinates are. Take x in the range [−5, 5], so y remains within [-3, 3]. I don't see a problem.  --Lambiam 17:56, 28 June 2022 (UTC)

If the slopes of the two lines are unequal (compare ratios), then they intersect. Otherwise if they have a point in common (solve equations), they are the same line. Otherwise, they are parallel. 2601:648:8202:350:0:0:0:FD2B (talk) 06:20, 2 July 2022 (UTC)

It is also easy to see that the two equations of the question have the same solution set: multiply both sides of the second one by 5 and simplify, and it turns into the first equation. But the question asks specifically to plot the graphs; given the limited size of paper sheets, this requires, with the most plausible procedure, the student to select the range of the abscissa; that of the ordinate then follows. I took the question to mean, "how is a student supposed to select this range?". For this specific question it does not matter; if the question had been about the two equations 47x + y + 2389 = 0 and 48x + y + 2438 = 0, not only the range of the abscissa but also the scales (aspect ratio) become important.  --Lambiam 10:37, 2 July 2022 (UTC)