Questions tagged [geometry]
For questions related to geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.
123
questions
38
votes
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 ...
3
votes
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 ...
4
votes
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 ...
13
votes
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 ...
4
votes
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 ...
16
votes
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
...
11
votes
0answers
216 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 ...
11
votes
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, ...
5
votes
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 ...
6
votes
3answers
212 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 $S \subset \mathbb{R}^3$&...
0
votes
1answer
144 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 ...
3
votes
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 ...
1
vote
0answers
103 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 ...
0
votes
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 ...
6
votes
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 ...
16
votes
3answers
450 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 ...
11
votes
3answers
274 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 ...
1
vote
2answers
95 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 ...
8
votes
6answers
260 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 ...
26
votes
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 ...
2
votes
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 ...
7
votes
4answers
161 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? ...
7
votes
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 ...
3
votes
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 $IP$. ...
28
votes
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 ...
1
vote
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?
0
votes
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 ...
18
votes
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.
4
votes
0answers
147 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 ...
-1
votes
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. ...
2
votes
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 ...
7
votes
2answers
136 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'...
4
votes
4answers
324 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 ...
8
votes
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," ...
3
votes
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 ...
4
votes
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 ...
3
votes
3answers
426 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?
33
votes
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
...
-3
votes
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 ...
2
votes
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 ...
6
votes
3answers
593 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 ...
4
votes
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. ...
4
votes
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 ...
4
votes
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 ...
2
votes
1answer
216 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 ...
12
votes
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 ...
3
votes
2answers
185 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 ...
5
votes
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, ...
28
votes
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!" (...
8
votes
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 ...
