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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20k 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 ...
4k views

Beautiful planar geometry theorems not encountered in high school

I would like to impress college students (undergraduates in the U.S.) that there is more to planar geometry beyond what they learned in high school. I would like to show them beautiful theorems they ...
11k 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 ...
10k 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 ...
28k 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 ...
6k 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!" (...
7k views

How to give my students a straightedge instead of a ruler

I'm having a "challenge" in my geometry classes getting students to avoid using rulers as measuring devices in constructions. As natural as that usage is, they're only supposed to use them to connect ...
3k views

Should figures be presented to scale?

I've been working with a teacher, helping her with tech. One of the things I help with is to convert PDF formatted quizzes or tests to DeltaMath for the students to take online. The issue that I face ...
16k 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 ...
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 ...
5k 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 ...
4k views

Why do we introduce the notion that triangles are "congruent" instead of just saying that they are "the same" or "equal"?

The assumed age of the students is 10-15 years old. What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to ...
3k 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 ...
9k 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.
992 views

Impossibility of trisecting the angle, doubling the cube and alike, what are reasons for or against discussing them in a course on algebra?

When I taught courses on algebra giving a first exposition to Galois theory I usually included some discussion of classical results showing the impossibility of constructing certain points with ruler ...
676 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 ...
6k 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 ...
1k 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 ...
536 views

Evidence for or against the claim that some students are "algebra people" and others are "geometry people"

Where I live and work, there is a widely-accepted and often-repeated claim that there are two kinds of students: "algebra people" and "geometry people". This claim sometimes gets expressed in ...
1k views

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Using number theory instead geometry to introduce proof in Basic School?

It seems there is an overall agreement that Geometry is the right place to introduce proof in Basic School. However, number theory (arithmetic) looks like to be a more simple environment (consider, ...
192 views

2D drawings of 3D objects in printed school textbooks: orthogonal or perspective?

There is a tradition in the use of orthogonal projections to represent 3D objects in printed school math textbooks. On the other hand, perspective projections represent better the way as we "see" real ...
1k views

Co-curricular lessons between geometry and chemistry?

My school is hyped about the promise of co-curricular education and they are giving the math and science teachers paid days off to develop lesson plans that synergize our learning goals. I'm on ...