# 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 ...
4answers
529 views

### Rhombuses, kites etc

As a high school teacher, I sometimes wonder about the usefulness of certain topics. Some topics seem to be in the textbook because they have always been there, not because they lead anywhere ...
3answers
242 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 ...
8answers
3k views

### Visual Pythagorean demonstration

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 ...
3answers
222 views

### Geometry textbook with an abstract algebra emphasis

I'm teaching a variety of undergraduate and graduate geometry classes (mostly for in-service teachers) which range from elementary axiomatic geometry to more advanced transformational geometry. I'm ...
5answers
1k views

### Should my 8th graders see a proof of the Pythagorean Theorem?

I've been teaching the Pythagorean Theorem in my 8th grade class, and I noticed something odd. In the book I'm using, the sequence goes something like this: Motivate the idea of distances on a grid ...
0answers
210 views

### Use of Lockhart's *Measurement* in a course?

I greatly admire Paul Lockhart's Measurement (Harvard Press). Many of you know him through A Mathematician's Lament. One review of Measurement said, “Here Lockhart offers the positive side of the ...
1answer
361 views

### 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, ...
4answers
334 views

### Why do standard geometry textbooks not start with trigonometry?

Throughout my geometry course, I was given many theorems and postulates, which I was were expected to memorize and apply. At the time, I sorta went along with it, but I couldn’t help but wonder where ...
3answers
210 views

### Why is it difficult to freely change between points and vectors?

I have noticed working with bright undergraduates that it is not uncommon for them to have difficulty easily converting between a point—say, a point $p$ on a surface $S \subset \mathbb{R}^3$&...
1answer
142 views

### Integrated math curriculum in different countries

One of the selling points of re-hashed American 1990s high school math programs is that they are "integrated", that is, combine algebra, geometry, statistics, trigonometry just like the European ...
1answer
160 views

### Geogebra for Blind People

I work in the University with students in a situation of disability, specifically, teaching them math and related things. I have a few students that are very visually impaired; they work with JAWS or ...
0answers
102 views

### Missouri EOC and the best Geometry book

I am a Missouri High School Geometry teacher. WE are adopting textbooks this year. I would like opinions on which books are most closely aligned with the Missouri Learning Standards because at the ...
3answers
203 views

### Good textbooks for a college Basic Geometry course?

I will be teaching geometry for the first time ever this summer. I teach at a community college, and we only offer this course in the summer. (Mostly high school students take it, but it is a college ...
4answers
176 views

### Group theory by geometry

I'm introducing my kids to the concepts of group theory. To make abstract things tangible, I'm trying the geometry way, adopting Arnold's in "Abel's Theorem", so far I've explained, by using symmetry ...
3answers
448 views

### Good lessons/activities for one-day subs

In my school district, and I'm sure most others, every teacher needs to have a set of "emergency lesson plans", in case they are sick or need to be out for a day, so that the substitute can have ...
3answers
273 views

### When Euclid was used as a textbook, what exercises did students do?

Until fairly recently, it was common for students in school to learn Euclidean geometry from a translation of Euclid. I get the impression that ca. 1700 this would have been in college and only for a ...
2answers
93 views

### Are questions on overlapping solids of revolutions without prior definitions and instructions fair given that there are divided interpretations?

If words of command are not clear and distinct, if orders are not thoroughly understood, the general is to blame. But if his orders are clear, and the soldiers nevertheless disobey, then it is the ...
6answers
258 views

### Book recommendations on mathematics education focusing on geometry

I will be teaching Euclidean geometry to future teachers, and I am feeling a bit lost (I know geometry, but I am not that familiar with mathematics education). Is there some recent (as concise as ...
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 ...
3answers
139 views

### How to give a good Geometry test? [closed]

Generally, in a Geometry test, you'd need to test proofs (Prove that triangle XYZ and ABC are congruent). On the other hand, proofs depends depends on theorems which depend on postulates, which are ...
4answers
160 views

### Making physical 3D models

I was thinking to make classroom illustrations of some 3D mathematical objects, such as graphs of 2 variable functions, minimal surfaces, etc. My question is, what would be a good way to go about it? ...
1answer
184 views

### Fun classroom exercise for mental rotation

I'm training to be a teacher and I am doing a maths lesson later next week. The topic is geometry, the students are 12-year-olds. More concretely, I've been given a selection of exercises that I may ...
0answers
131 views

### How to explain angle hunting to students

$I$ is a point of the circle of diameter $JK$. The perpendicular bisector of $JK$ cut the semi-circle not containing $I$ at $M$. Let $N$ and $P$ be the orthogonal projections of $M$ on $IJ$ and $IP$. ...
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 ...
0answers
50 views

### Geometry sample tests

I am teaching intro to Geometry using Moise and Downs textbook. It is an excellent text but somewhat old. Does anyone know if there are sample tests that are available for use with this textbook?
0answers
62 views

### Recommend a website for creating geometric figures

I want to find a website where I can enter the names of vertices of a polygon, specify which diagonals should be depicted, and specify the measures of certain angles, and have the website generate a ...
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.
0answers
146 views

### Intuition: 5 regular polyhedra, 6 regular 4-polytopes, and then 3 regular d-polytopes

I have struggled to offer an intuitive explanation (to U.S. college students) why the number of regular polytopes in dimension $d$ is: $d=2$, number: $\infty$. $d=3$, number: $5$, the five Platonic ...
1answer
72 views

### How should I solve this geometrical problem [closed]

One of my students found this problem and gave it to me in order to help him but I cannot really think of something that will help for the solution. So, this is the problem: ABC is a random triangle. ...
0answers
102 views

### Why does result depend on procedure in my calculation of surface area using Guldin? [closed]

At present, I teach Guldin's rules for surface and volume of rotation, and give an example task from the textbook. The textbook uses procedure 1 (below) for calculation (below), but I advocate that ...
2answers
135 views

### Drawing vs Constructing

How would you explain to students the difference between drawing and constructing? "Accuracy" seems to be a go to word, but that's not really what the difference is. I want to say more, but I also don'...
4answers
321 views

### Teaching congruent triangles non-rigorously

I've just started teaching congruent triangles to a class of 14/15 year olds in the UK. All that they are required to know for the purpose of national exams here is that two triangles are congruent if ...
2answers
228 views

### Resource to supplement to Euclid's Elements

I am an instructor at a mid-sized American university, preparing to teach a two-quarter geometry course for junior and senior math majors. My plan is to use Hartshorne's "Geometry: Euclid and Beyond," ...
6answers
234 views

### Multidisciplinary problem

I am looking for ideas for an activity for high school students, which involves plane geometry and another field, such as algebra, series, etc... For example, in junior high there is a nice activity ...
2answers
135 views

### How are geometric proofs related to geometric pictures?

When teaching geometry it is common to use pictures/figures to "show" the problem and its solution. It's also common to say things like "more than one figure can be shown which demonstrates the same ...
3answers
425 views

### Which book should I refer to for analytical solid geometry?

I am an undergraduate student and since this is a site of math educators, I thought of putting this question (more accurately a query) here. Can you list some good books on analytical solid geometry?
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 ...
1answer
89 views

### When a geometrical figure a special case of another [closed]

Squares are special types of rectangles. Are circles special types of ellipses/ovals? Are cones special types of pyramids? I guess the answer is no because of the 2D basis: circles are not special ...
1answer
222 views

### Are kindergartners supposed to be steered from squares being rectangles?

Question 1: What are the literature, status, debates, references, etc regarding this matter please? Apparently, some (woohoo weasel words!) consider that squares are rectangles too advanced a topic ...
3answers
591 views

### In what curricula are “rectangles” defined so as to exclude squares?

Most contemporary curricula define the word "rectangle" inclusively, so that all squares are automatically rectangles. Are there curricula in which this convention is not followed? That is, are ...
0answers
94 views

### Why define the names of quadrilaterals so that some categories (rhombus and rectangle) intersect and some (kite and trapezoid) are disjoint?

We're using Pearson's Geometry in my class. As terms are defined there, Parallelograms include Rhombi (congruent sides), Rectangles (right angles), Squares (congruent sides and right angles, i.e. ...
3answers
168 views

### Resources for precalculus applications

Do you know any good sources of free/open application-style problems for the precalculus level? I would like to use an OER precalculus book, but the few I am most happy with seem to lack (what we ...
5answers
115 views

### Books and worksheets on symmetry

At a local Math Circle, I loved some problems worked out through a hinged mirror to illustrate symmetry. I bought a hinged mirror from hand2mind.com, and am looking for some material, ideally books ...
1answer
215 views

### Learning High School Geometry in Ten Days

I would like to attempt this, as I want to place out of geometry next year. It is imperative that I do it now. How should I go about doing this? I have a copy of Elementary Geometry for College ...
6answers
543 views

### Can we explain to undergraduates how points make a line?

Many of my students arrive in college believing that lines are (in some way) made out of points. They also believe that points have no length. They want to know how a bunch of zero length points ...
2answers
184 views

### Is the Nomenclature of Triangle Congruency Proofs Consistent?

My Geometry class is doing triangle congruency proofs these days. In general, we find three pairs of congruent parts (sides or angles) in two triangles; we show that these congruencies reveal that the ...
1answer
229 views

### Applications of notable points and lines of a triangle

I am currently starting to teach math to highschool kids who don't do well on their own, and I'm teaching a guy about notable points and lines of a triangle (incenter, centroid, circumcenter, ...
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!" (...
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 ...