If we compose a glide symmetry to itself what is the result? Two different glide symmetries?

Talon Mcbride
2022-07-26
Answered

If we compose a glide symmetry to itself what is the result? Two different glide symmetries?

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Clarissa Adkins

Answered 2022-07-27
Author has **16** answers

Let the glide reflection be T. Without loss of generality the reflection part of T' is reflection in the y-axis. Assume that the translation part is by the vector (a, b).

The reflection takes (x,y) to (-x,y). The translation part now takes us to (-x+a, y+b). So T takes (x,y) to (-x+a, y+b).

Do it again. The reflection part takes (-x+a, y+b) to (x-a,y+b), and the translation part takes this to (x,y+2b). So T^2 is translation parallel to the y-axis by 2b.

The reflection takes (x,y) to (-x,y). The translation part now takes us to (-x+a, y+b). So T takes (x,y) to (-x+a, y+b).

Do it again. The reflection part takes (-x+a, y+b) to (x-a,y+b), and the translation part takes this to (x,y+2b). So T^2 is translation parallel to the y-axis by 2b.

asked 2022-06-24

The problem is: Given parallelogram ABCD with diagonals $\overline{\mathrm{A}\mathrm{C}}$ and $\overline{\mathrm{B}\mathrm{D}}$ intersecting at E. If m$\mathrm{\angle}\text{}AEB$=60 degrees, m$\mathrm{\angle}\text{}CAB$=30 degrees, and AB=18, find AD.

This problem seems simple, and I presume that you use the properties of special right triangles; however, I can't seem to get the right answer. The answer is 6 $\sqrt{\text{}}21$. Thank you!

This problem seems simple, and I presume that you use the properties of special right triangles; however, I can't seem to get the right answer. The answer is 6 $\sqrt{\text{}}21$. Thank you!

asked 2022-07-26

A soccer player passes the ball from a point that is 18 yards from the endline and 12 yards from the sideline. The pass is received by a teammate who is 42 yards from the same endline and 50 yards from the same sideline, as shown in the figure. How long is the pass? (Round your answer to the nearest yard.)

asked 2022-07-18

Original order pairs: $(\sqrt{5},\sqrt{3})\text{}\text{}(-\sqrt{20},-\sqrt{12})$

Work for finding midpoint:

$M=\frac{(\sqrt{5}+-\sqrt{20})}{2}\text{}\text{}\frac{(-\sqrt{3}+-\sqrt{12})}{2}$

Work for finding midpoint:

$M=\frac{(\sqrt{5}+-\sqrt{20})}{2}\text{}\text{}\frac{(-\sqrt{3}+-\sqrt{12})}{2}$

asked 2022-04-30

The hopf map in terms of quaternions is defined as

$h:r\mapsto {R}_{r}({P}_{0})=ri\overline{r}$

where r is a unit quaternion and ${P}_{0}=(1,0,0)$ is a fixed point. If a point $r\in {S}^{3}$ is sent by the Hopf map to the point $P\in {S}^{2}$ , a formula can be derived for a particular representation for the cosets. In my case, I want to derive a formula for the ${180}^{\circ}$ rotations around an axes through i and other points in ${S}^{3}$ .

$h:r\mapsto {R}_{r}({P}_{0})=ri\overline{r}$

where r is a unit quaternion and ${P}_{0}=(1,0,0)$ is a fixed point. If a point $r\in {S}^{3}$ is sent by the Hopf map to the point $P\in {S}^{2}$ , a formula can be derived for a particular representation for the cosets. In my case, I want to derive a formula for the ${180}^{\circ}$ rotations around an axes through i and other points in ${S}^{3}$ .

asked 2022-05-29

I want to show that $2{p}_{n-2}\ge {p}_{n}-1$...

Bertand's postulate shows us that $4{p}_{n-2}\ge {p}_{n}$ but can we improve on this?

any ideas?

Bertand's postulate shows us that $4{p}_{n-2}\ge {p}_{n}$ but can we improve on this?

any ideas?

asked 2022-05-27

How to integrate ${\int}_{0}^{\pi /2}\frac{\mathrm{sin}(x)}{\mathrm{sin}(x+\frac{\pi}{4})}\mathrm{d}x$ using substitution $x=\frac{\pi}{2}-y$ ?

asked 2022-05-09

Suppose I have this boolean expression:

W'XYZ + WX'YZ + WXY'Z + WXYZ' + WXYZ

How would I go about simplifying this without using a K-map? Using K-map, the simplified form is XYZ + WXY + WXZ + WYZ. I read about the redundancy theorem somewhere, would rather not use that as well.

W'XYZ + WX'YZ + WXY'Z + WXYZ' + WXYZ

How would I go about simplifying this without using a K-map? Using K-map, the simplified form is XYZ + WXY + WXZ + WYZ. I read about the redundancy theorem somewhere, would rather not use that as well.