# Questions tagged [geometry]

For questions related to geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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33answers
14k views

### Real-world examples of more “obscure” geometric figures

As part of my secondary geometry class I like to hook students by presenting real-world examples (usually images I find online or have taken myself) of different geometric shapes from real life. For ...
16answers
10k views

### Why are triangles so prevalent in high school geometry?

A colleague and I recently discussed what we call the "Triangle Trap." High school geometry covers a very large unit reflecting the common core: Classifying Triangles Triangle Angle Properties ...
10answers
9k views

### Is this homework problem on counting triangles within a 4x4 grid too vague?

My six-year old daughter was given this maths problem for her homework: Given a regular square grid of 4 × 4 dots, how many different triangles with one dot in the middle can you draw? We were ...
11answers
21k views

### Why should kids learn how to use a compass and straightedge, and not rely on a drawing program?

I am curious why it is necessary for people to learn how to use compasses and straightedges in geometry, and not just rely on a drawing program. I have a couple ideas, but I might be missing ...
10answers
4k views

### Is Euclid dead? or Should Euclidean geometry be taught to high school students?

Apparently Euclid died about 2,300 years ago (actually 2,288 to be more precise), but the title of the question refers to the rallying cry of Dieudonné, "A bas Euclide! Mort aux triangles!" (...
17answers
13k views

### Given a 3 4 5 triangle, how do you know that it is a right triangle?

Without knowing the Pythagorean theorem, and in presenting reasons why the theorem might be true (without giving a full proof), is there any way to give examples of triangles that are intuitively ...
7answers
3k views

### Why do we care about multiple proofs of the same theorem?

I am teaching a math appreciation course to high school students who are approximately 17 years old, in their last year of high school, and who do not believe they will choose a STEM major in ...
10answers
4k views

### Pi or Tau? How should the circle constant be taught?

Tau ($\tau = 2 \pi$) has more merits in its application, but pi is the established standard in industry and education. Is the trade-off of teach-ability of circle concepts worth the subsequent ...
3answers
420 views

### At what point is it a disservice to pass someone on to the next math class?

Background information I'm currently teaching common core geometry, which assumes that a student has algebraic knowledge coming in. Clearly, we shouldn't expect students to retain everything from ...
8answers
2k views

### Are there disadvantages to teaching complex numbers as purely geometrical objects?

Complex numbers are, or at least were to me, generally introduced like this: There's no number whose square is negative. That's a shame! Well, whatever - we'll make one up! Set $i^2=-1$ and declare ...
4answers
972 views

### Teaching manifolds to high schoolers

I would like to introduce the concept of a manifold to a high school student. This person isn't familiar with the axioms of set theory nor topology. However, despite these deficits, I would like to ...
10answers
5k views

### A parabolic arc is not semicircular. But students think so

I'm teaching a Calc 2 class now (integration and applications) and I'm surprised that more than a handful of students seem to think the graph of $y=x^2$ on $-1\le x\le 1$ is part of a circle! Here is ...
12answers
8k views

### How to explain that we live in a three-dimensional world?

How does one explain, clearly and simply, that we live in a three-dimensional world? The explanation has to be understandable for a twelve year old child.
11answers
1k views

5answers
193 views

### Extensions beyond Euclidian Geometry for Secondary students

My secondary geometry class is really amazing and is likely going to finish everything I have for the curriculum with a few weeks left in the school year. I was thinking to use these last few weeks ...
4answers
1k views

### Secondary Geometry Curriculum Sequencing?

I am currently student teaching, and the main class that I am focusing on is a secondary geometry class. I am currently following my classroom mentors curriculum sequence which looks something like: ...
2answers
214 views

### Teaching geometric transformations through fractals?

In roughly two weeks, my secondary geometry class will have reached the part of the year where we discuss geometric translations: translation, rotation, and reflection. Dilation i am going to use as ...
5answers
230 views

### How do you explain straightness to a 5-year-old?

How do you explain straightness to a 5-year-old? I am having a hard time trying to explain straightness to little kids. I have been asked, "How do you know that the ruler is straight?" Are there any ...
3answers
748 views

### Gifs of finding the volume of 3d shapes?

I'm looking for some animations (videos or gifs) of finding the volume of different 3d shapes. It would be super helpful if I could find something which stacks unit cubes into a rectangular prism to ...
2answers
275 views

### Learning Math like Euclid

I'm posting this here as it's off-topic for the Math stack exchange, and I'm hoping there will be some educators here that can point me in the right direction. I enjoyed watching the YouTube series ...
2answers
197 views

### Coverage of Fundamentals of Lines and Planes

I was helping a high school student with some fundamental concepts of planes and lines, when I realized I am rusty on some definitions myself. I found some minimal coverage in his high school math and ...