# 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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### interesting/challenging geometric constructions for gifted secondary students

I have three students in my secondary geometry class that just destroy everything I throw at them. I tasked them with writing the word problems for their midterms and one of the three wrote simply "...
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 ...
406 views

### Is there an elementary way to explain that a map of the earth cannot preserve distances?

I am teaching a short "topics in geometry" course to future high school math teacher in France. I plan to cover some spherical geometry. I will be treating the following topics: volume of the ball ...
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 ...
1k views

### Project/Assessment based on Flatland for Secondary Geometry Class

One of my favorite books is Flatland by Edwin Abbott, which is incredibly rich in geometric concepts especially relating to dimensionality. I would really like to assign it to my secondary geometry ...
3k views

### How Can I Motivate Geometric Constructions?

When starting compass and straightedge geometric constructions in my grade 8-9 maths classes, I usually begin by mentioning a little about Euclid and the fact that constructions have been done for ...
3k views

### Notation of points with coordinates

At least in Germany, nearly all teachers and textbooks use the notation $$P(x,y)$$ for the point $P$ with coordinates $x$ and $y$. My own math professors at university always cried about this, as the ...
975 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 ...
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.
259 views

### Helping students use constructions in geometry

I work as a teaching assistant in a high school and geometry gives most students headaches. I emphasize understanding the problem by constructing lines and using elementary properties to arrive at ...
933 views

### Fun Activities/Games Before a Break/Between Units for Secondary Geometry

I have been planning ahead and it looks like i will have a solid three to four days before the winter break where we wont really be in a unit. We will have just finished a unit and i do not want to ...
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: ...
245 views

### Explanation challenge: Why is a spiral ray-gun difficult to aim?

In an off-topic discussion, I tried to explain to a student why a "ray-gun" that (somehow!) shoots a ray that followed a spiral path would be much more difficult to aim at a particular target (point ...
122 views

### Intuitive explantion: What is a Finsler metric?

Neither of the two most evident sources, MathWorld: "Finsler Metric." Wikipedia: "Finsler Manifolds." seems to provide me with the high-level intuition that I could convey to students in ~10 minutes....
403 views

### Will presenting non-Euclidean geometries to students before Euclidean geometry give them a better intuition about shapes on the plane?

This question is related to Is Euclid dead? or Should Euclidean geometry be taught to high school students?, but I am not asking about whether Euclidean geometry should be taught at all, but whether ...
156 views

### Explaining the algebra behind a problem in computer geography

For work, I tend to have to explain quantitative ideas to people with only some informal computer science training. Yesterday, my friend wanted to draw a map on his computer and was concerned we ...
723 views

### Wiggins' question #12

There's an interesting read: Conceptual Understanding in Mathematics by Grant Wiggins. In that text the author proposes "a test for conceptual understanding" which should be given "to 10th, 11th, and ...
731 views

### Symmetry - practical usages

My girlfriend is studying to become a math teacher, and asked me what I have ever used symmetries for. I'm a web developer, and do some designing from time to time, so I answered that symmetry have ...
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!" (...
303 views

### Adoption / penetration rates for dynamic geometry software in secondary school

Dynamic geometry software (DGS) has been around for decades; Geometer's Sketchpad (not the first, but probably the most well-known commercial product) has been around since 1986. Wikipedia lists more ...
854 views

### Reasons to teach Thales' theorem

In a classical course on Euclidean, compass-and-ruler geometry, Thales' theorem has always had a prominent place. However, as the Wikipedia article says, It is equivalent to the theorem about ...
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 ...
250 views

### Appropriate education level for this geometry problem

What's the appropriate education level for the following concise but non-trivial geometry problem? Points $A$, $B$, $C$ are collinear; $\|AB\|=\|BD\|=\|CD\|=1$; $\|AC\|=\|AD\|$. What is the set ...
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 ...
I know that there is a visual demonstration of $a^2+b^2=c^2$ using a smalĺ piece of paper, but there are also a lot of variations. Which visual or drawing demonstration of the Pythagorean theorem can ...