Questions tagged [geometry]
For questions related to geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.
134
questions
2
votes
2answers
31 views
What are strategies for teaching that the altitude of a right triangle creates two similar triangles?
If you draw the altitude to the right triangle as shown, it is easily seen that $$\triangle KLM\sim\triangle KNL\sim\triangle LNM.$$ This in turn leads to several interesting proportional relations ...
2
votes
3answers
137 views
Mnemonic for volume of cone $V=\frac{1}{3}\pi r^2 h$ [closed]
Does anyone have a good mnemonic for the volume of cone formula: $$V=\frac{1}{3}\pi r^2 h?$$
3
votes
2answers
157 views
Introducing quadric surfaces in high school
I am presenting an enrichment session on 3D geometry and quadric surfaces to able 15-year-old secondary school students. They know algebra but not calculus. They have learned about equations of ...
4
votes
2answers
395 views
Euclid Book 1 Proposition 4 [closed]
In Euclid's The Elements, Book 1, Proposition 4, he makes the assumption that one can create an angle between two lines and then construct the same angle from two different lines. I do not see ...
8
votes
3answers
675 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 ...
0
votes
1answer
183 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 ...
1
vote
1answer
93 views
How to teach geometric patterns? [closed]
I would like to know how to teach geometric patterns in secondary school. I want to elaborate worksheets, which could include different kinds of strategies related to this topic.
Are there resources ...
34
votes
11answers
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 ...
3
votes
0answers
126 views
Cinderella vs. GeoGebra
I would be grateful for a comparison between
the capabilities of Cinderella and
Geogebra, for teaching
at all levels, but especially at the college/university-level.
I became a reasonably adept user ...
4
votes
1answer
187 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 $IP$. ...
10
votes
4answers
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 ...
39
votes
35answers
15k 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 ...
-1
votes
4answers
264 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 ...
27
votes
12answers
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 ...
2
votes
1answer
126 views
Recommend a website for creating geometric figures
For teaching geometry, it could be useful to have a website where one can enter the names of vertices of a polygon, specify which diagonals should be depicted, and specify the measures of certain ...
2
votes
2answers
180 views
High school maths textbook for talented students
I am looking for a math textbook. I'm 15 and I'd like to complete
algebra 2 geometry and perhaps something about probability/ number theory or trigonometry would be nice too. Later I wanna do ...
8
votes
1answer
534 views
An alternative to “two column” geometry proofs
I'm a high school teacher in New York State (US), starting in on my first year of teaching Geometry. One of the things that really intrigues me is that the Regents exam (the state-mandated final exam)...
4
votes
4answers
545 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
249 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
236 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
...
10
votes
0answers
275 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
374 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
347 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 ...
7
votes
3answers
231 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 $S \subset \mathbb{R}^3$&...
4
votes
1answer
195 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
113 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 ...
6
votes
4answers
188 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
457 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 ...
12
votes
3answers
303 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 ...
2
votes
2answers
102 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 ...
9
votes
6answers
318 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
148 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
217 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
194 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 ...
28
votes
11answers
22k 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 ...
2
votes
0answers
52 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?
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
151 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
78 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
104 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
189 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
414 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
269 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
282 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
509 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
...
