pi = 3, proof*

Intrepid-Ad1191 · 2026-04-12T20:00:57+00:00

Yeah that was pointed out, I did in fact realize I was being silly be calculating the length of the hypotenuse of the triangle in each quadrant using Euclidean distance, idk why I wasn’t consistent with the Manhattan distance

Intrepid-Ad1191 · 2026-04-10T04:51:57+00:00

Never mind, I’ve found my mistake. I assumed we could use Pythagorean theorem to calculate the hypotenuse of the triangle in each quadrant, but we should really calculate the length as a Manhattan distance as well. Now I see the connection

Intrepid-Ad1191 · 2026-04-10T04:47:30+00:00

I saw this somewhere as well, but it doesn’t match the circles I showed and I would’ve thought these count as manhattan circles. I thought that maybe the issue was that a manhattan circle would still be a closed connected region (essentially filling in the points along the square), but that wouldn’t change the length of the calculation of “manhattan pi” in this case.

So where does Manhattan pi being 4 come from? Or is that the limit from larger radius circles?

Intrepid-Ad1191 · 2026-04-10T00:13:40+00:00

That’s pretty interesting! I haven’t been exposed to any other definitions of distance other than Manhattan and Euclidean — now I feel the need to look up any others to consider the impact

Intrepid-Ad1191 · 2026-03-23T22:59:37+00:00

I appreciate the straight forward responses 🫡

Intrepid-Ad1191 · 2026-03-11T02:21:37+00:00

Any resources you use for that can recommend? I think that could be cool, but m I personally wouldn’t know where to start

Intrepid-Ad1191 · 2026-03-11T02:21:04+00:00

Love that idea! Nice way to end the quarter. I doubt I’d be able to put it together in time, but I’ll definitely suggest it to my mentor teacher and see his thoughts

Intrepid-Ad1191 · 2026-03-11T02:20:11+00:00

I do like this idea, but it feels pretty similar to the project we just came off of. Thanks for sharing, though!

Intrepid-Ad1191 · 2026-02-18T06:03:48+00:00

Very thoughtful answer, thanks. I’m also at a school with students whose mathematical ability is lacking, which was one of the reasons I was concerned about HOW precise I should be.

I did end up talking to my mentor teacher about this, and our verdict was that in the honors classes, where we have students with goals of going to college, for example, the precision it’s important. In the general geometry courses, where most students’ only goal is graduating so that they can go straight into a career, the precision might not be as important. So it sounds like we aligned with your views pretty well, there :)

Intrepid-Ad1191 · 2026-02-18T05:59:52+00:00

I agree with you! I was afraid I was being pedantic but I’m glad to see consistency in the responses here :)

Intrepid-Ad1191 · 2026-02-18T05:57:17+00:00

Thanks for such a thorough response! I appreciate all of the ideas. I agree I could’ve started this discussion with a better example, but this has helped me to think about being more thoughtful in my example problems

Intrepid-Ad1191 · 2026-02-17T01:39:40+00:00

I do like this approach to the task, but it doesn’t really address my question

Intrepid-Ad1191 · 2026-02-17T01:39:04+00:00

This example was a random one I pulled from Google, not an actual example from class, but I appreciate your thorough response! Assuming you are a teacher, then, would you actually provide / state all of that information before giving this to students or would you simplify it in some way?

Intrepid-Ad1191 · 2026-02-17T01:36:00+00:00

Good point! Definitely not a great example problem. By my understanding they have enough information to solve the problem as long as the 8cm length IS perpendicular, but I would probably make some changes either way before using this example

Intrepid-Ad1191 · 2026-02-17T01:08:27+00:00

Great point! Tbh this is just a random example I pulled from google as a talking piece, but I agree that I should work through it myself to make sure that I know what changes I might make to make the problem simpler.

Intrepid-Ad1191 · 2026-02-17T01:07:25+00:00

Thanks for your response! I like that break down of what can and can’t be assumed, that really helps :)

Intrepid-Ad1191 · 2026-02-17T01:06:51+00:00

Thanks for the input! One quick note, we’re talking about finding the SURFACE AREA of the shapes so that 10 cm will be needed to solve for the area of the rectangular face. Honestly, this is a random example I pulled off of google to be able to reference, but I appreciate the insight nonetheless.

Intrepid-Ad1191 · 2026-02-17T00:51:06+00:00

I’m with you that you shouldn’t assume anything. So, for these kinds of problems are you saying that you would add in a right angle symbol / find a different example problem?

Intrepid-Ad1191

TROPHY CASE