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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27
votes
10answers
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 ...
4
votes
4answers
235 views

Can we define length and perpendicularity not via an inner product?

A natural way to reason about Euclidean geometry using modern mathematical language is to define Euclidean space as an affine space $A$ directed by a finite-dimensional real vector space $V$. However, ...
6
votes
2answers
135 views

Is $\overline{AB} \cong \overline{BA}$ usually taught as an instance of the symmetric property of congruence?

I have been tutoring a wide range of math subjects for many years. Recently, I began tutoring a girl in high school geometry (in California, for context). This semester of the course is starting with ...
9
votes
3answers
1k views

Definition of Trapezoid

From one textbook we use in our High School - Transcription: A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases of the trapezoid. And from ...
11
votes
3answers
274 views

How to teach the Pythagorean theorem in a satisfying way to high school students?

I've been pretty dissatisfied with the way the Pythagorean theorem is usually taught, mainly for two reasons: The chosen proof feels like magic and I don't feel like I have a better understanding of ...
1
vote
1answer
186 views

US High School Geometry: What are all the “reasons” allowed in two column proofs?

For a project I am considering on geometry in US high schools, I need a list of all the reasons that are usually allowed in two column geometry proofs there. I have a bachelor's degree in math and ...
3
votes
4answers
571 views

What is an algebraic explanation of why the product of the slopes of perpendicular lines is $-1$? [duplicate]

Q: What is a succinct, clear and purely algebraic explanation of why the product of the slopes of perpendicular lines is $-1$? Here I am aiming for high-school students (in the U.S.). I have a purely ...
9
votes
5answers
2k views

Is there a name for paths that follow gridlines?

I'm writing up an activity where students are looking at pathlengths that follow along gridlines. Is there a word or phrase that is commonly used to describe those paths, but doesn't include ...
5
votes
3answers
319 views

Is there online geometric construction software that models physical constructions?

In this weird pandemic school year, I'm doubly interested in technology integration to help my virtual (high school) students as much as my in-person students. I've been particularly eager to get ...
1
vote
1answer
171 views

Which Geometry book is more rigorous/harder?

Can anyone please tell me if the AOPS (Art of Problem Solving) Geometry is more rigorous/difficult generally than a book called "Geometry for Enjoyment and Challenge" by authors Rhoad, ...
9
votes
1answer
200 views

College undergraduate geometry courses

I am interested in learning how a course in geometry is employed today at undergraduate colleges/universities in the U.S. On the one hand, such a course seems to serve as an optional (rarely required) ...
1
vote
0answers
41 views

Exercises for explaning homothety, homothetic center, similarity on line and plane, free vector and vector space

I need the collection of exercises for such topics as: maps and transformations, composition of maps homothety, rotation homothety, homothetic center similarities of the line and the plane free ...
8
votes
6answers
4k views

Why we have to be so precise in Geometry?

Previously I've explained some basic things of graphs to my kid, such as planar, $V-E+F=2$. Now when I introduce geometry, he asked, "Why we have to be so precise in Geometry?" Indeed, in ...
1
vote
1answer
90 views

What books are good to study Solid Mensuration?

Preferably I want those that contain the following topics: Solid Figures Polyhedrons Prisms Pyramids Prismatoid Truncated Prisms Cylinders Cones Spheres I've been ...
1
vote
2answers
229 views

Workbooks for advanced high school math topics

I'm looking for advanced workbooks and exercises for working in class (math high school/undergraduate level) covering the following topics (or some of them): Logic and sets (propositional calculus, ...
10
votes
11answers
4k views

Ideas for explaining 4D and higher dimensions

I introduced the hypercube (to undergraduate students in the U.S.) in the context of generalizations of the Platonic solids, explained its structure, showed it rotating. I mentioned Alicia Stott, who ...
3
votes
2answers
174 views

Should we stop using traditional compass in schools & start/encourage adopting compasses like “Slide N Measure” or “Safe-T” compasses instead?

I think using the traditional compass with those styluses that can literally be used to hurt or accidentally hurt someone are very dangerous. Most people don't use these in day-to-day life anyways, ...
12
votes
2answers
175 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 ...
5
votes
5answers
2k 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 ...
1
vote
3answers
183 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: $$V=\frac{1}{3}\pi r^2 h?$$
4
votes
2answers
453 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 ...
3
votes
2answers
172 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 ...
1
vote
1answer
100 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 ...
4
votes
1answer
292 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 ...
36
votes
12answers
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 ...
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 ...
2
votes
2answers
731 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 ...
28
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 ...
8
votes
1answer
667 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)...
6
votes
8answers
695 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 ...
10
votes
0answers
429 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 ...
7
votes
3answers
248 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 $S \subset \mathbb{R}^3$&...
5
votes
1answer
332 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
votes
1answer
286 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
0answers
117 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
222 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 ...
2
votes
2answers
109 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 ...
14
votes
4answers
407 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 ...
4
votes
3answers
274 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 ...
-1
votes
4answers
298 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
396 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 ...
9
votes
6answers
460 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 ...
2
votes
3answers
156 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
418 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
215 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 ...
4
votes
1answer
192 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 $IP$. ...
2
votes
0answers
53 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?
2
votes
1answer
138 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 ...
4
votes
0answers
156 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
84 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. ...