All questions with tag [math: geometry]


how was this angle found?

This is a remedy from a publication entailing trusses (in statics), I do not recognize just how they located the angle $\theta$. What is their method? This is the offered trouble: (the offered sizes vary a little bit in between the trouble in guide and also the remedy guidebook)
2022-07-25 17:47:21

On Constructions by Marked Straightedge and Compass

Pierpont proved that a regular $n$-gon is constructible by (singly) marked straightedge and compass if and only if $n = k \, p_1 \cdots p_{s}$, where $k = 2^{a_1} 3^{a_2}$ for $a_i \geq 0$ and $p_i = 2^{b_1} 3^{b_2} + 1 > 3$ is prime with $b_i \geq 0$. It has been known since the time of Archimedes that a marked straightedge allows for an...
2022-07-25 17:47:10

How do I calculate the length of a vertical offset of the major axis in an elllipse?

Please forgive my terms if it is inaccurate. In the layout listed below, for well-known values of X, Y and also Z, I am require to compute the value (size) of M. (It is not research, it is for an SVG computer animation ) Thanks beforehand.
2022-07-25 17:44:54

Relations between metric on H and the disc model

In the book "Modular Forms" by Miyake one finds the definition of some obscure 'thing'. He calls it a metric on $\mathbb{H} = \{z \in \mathbb{C} : \operatorname{Im}(z) > 0 \}$. The following is defined: $$ds^2(z) = \frac{dx^2 + dy^2}{y^2}$$ Now the first thing that bothers me is that he writes a dependency of '$z$' while $dx$ an...
2022-07-25 17:44:03

How to find radius of covering of sphere?

Suppose we have unit sphere in space $R^n$ which is inscribed sphere of a hypercube. Let we have epsilon-net on the facets of hypercube. For examle, in 3-D this epsilon-net is given as the set of points with coordinates: $(-1,\hspace{2mm} -1+i*h,\hspace{2mm} -1+j*h)$ $(1,\hspace{2mm} -1+i*h,\hspace{2mm} -1+j*h)$ $(-1+i*h, \hspace{2mm} -1,\hsp...
2022-07-25 17:43:44

How to calculate the coordinates of a line which is parallel with another where they intersect with a horizontal?

I have 2 identical lines and also I recognize the works with for among them where it interesects with a straight line on the leading and also a straight line under and also the range in between them. What I am attempting to fathom is just how to exercise the works with where the 2nd parallel line converges with claimed straight lines. Below is...
2022-07-25 17:43:30

Finding point coordinates of a perpendicular

Given that I recognize the factor works with of factor $A$ and also factor $B$ on sector $AB$ and also the anticipated size of a vertical sector $CA$ (vertical over $AB$), just how do I compute the factor works with of the factor $C$?
2022-07-25 17:43:26

Affine form of a dual to the Sylvester-Gallai theorem?

The following question came up in the course of . Let $S$ be a set of lines in the real affine plane, with the following properties $S$ is finite, there are at least two points in which some pair of lines from $S$ intersect. Does this imply that there is at least one point where exactly two lines of $S$ intersect? Another way of formulating th...
2022-07-25 17:42:06

Represent lengths rectangle using given terms

In a rectangle, $GHIJ$, where $E$ is on $GH$ and $F$ is on $JI$ in such a way that $GEIF$ form a rhombus. Determine the following: $1)$ $x=FI$ in terms of $a=GH$ and $b=HI$ and $2)$calculate $y=EF$ in terms of $a$ and $b$.
2022-07-25 17:21:32

Euler's Line of a medial triangle

I have the following problem with a comment below on the steps that I took so far. Here is the example: Let triangle ABC be any triangle. The midpoints of the sides in Triangle ABC are labeled $A', B', C'$ of sides: $BC, CA, AB$. Let $D, K, I$ be the circumcenter, centroid and orthocenter, $D, K, I$. Let $ D', K', I'$ be circumcenter, ortho...
2022-07-25 17:20:33

orientability of the möbius strip using homology

I read in Hatcher is "Algebraic topology" publication concerning orientability of topological maifolds making use of homology. currently I would love to recognize just how one can use this to show that the möbius strip is not orientable? i have no suggestion.
2022-07-25 17:18:46

Theorem related to Triangle.

Prove that in triangular $ABC$ if angle bisectors attracted from $B$ and also $C$ are conforming after that $AB=AC$.
2022-07-25 17:18:35

truss structure geometry - geometric induction?

This could be an actually straightforward Geometry regulation that I'm missing out on, yet I can not recognize just how in this trouble they instantly recognized to expand the truss to factor X and also recognized that it was an added 2 little triangulars. I recognize that if I were to address the whole truss making use of the regular devices li...
2022-07-25 17:17:25

clock related challenge

An individual leaves his residence in between 4.00 and also 5.00 pm. He meticulously keeps in mind the placement of the minute hand and also hr hand when he leaves your house. He returns back in between 7.00 and also 8.00 pm.He notifications that the hr hand and also the minute hand have actually specifically swapped their placements. What time ...
2022-07-25 17:15:16

Maximize lateral surface of a square pyramid in a sphere

I need to address the adhering to trouble. Job - summary: A round with the distance of $10$ has a pyramid with the topmost side surface area ($M_{max}$). Locate $M_{max}$. I require 2 terms. Among them is the adhering to, yet I do not locate a 2nd one.
2022-07-25 16:58:08

Are there simple examples of Banach spaces with no non-trivial Clifford Isometries?

By a Banach room $X$ I suggest, a full normed vector room and also by a Clifford isometry I suggest a surjective isometry $\gamma$ of $X$ such that the range $d(\gamma x, x)$ is constant on $X$. Naturally, $\gamma$ works as a "translation" so Clifford isometries are occasionally called Clifford translations. As an instance, in Euclidea...
2022-07-25 16:52:16

Application problem on volume of Pyramid and cylinder

The quantity of a pyramid with an isosceles triangular base is $240 cm^2$ and also it is elevation is $20 cm$. The base of the base triangular is $6 cm$. What is the size of the various other 2 sides of the base? Jerry is loading round canisters with size $6$ in. and also elevation $10$ in. snugly right into a box that gauges $3 ft \times 2...
2022-07-25 16:52:08

Golden Ratio within quadrilateral

Could you aid with a Euclidean aircraft geometry problem?¢ If WXYZ is a rectangular shape, U gets on XY and also V gets on YZ. We understand that the adhering to triangulars are of equivalent location: triangular WXU, triangular UYV, triangular VZW. If a = XU, b = UY, c = YV, d = VZ, after that confirm that b/a will certainly coincide as c/d whi...
2022-07-25 16:43:14

Prove there exists a triangle without using Euclidean Parallel Postulate

Let $a$ and $b$ be real numbers where $0 < a< b<180$. Let $A$, $B$, $D$ be points so $A$-$B$-$D$. Part 1: Prove there exists a triangle $ABC$ where measure of angle $CAB$ is $a$ and measure of angle $CBD$ is $b$. How do I prove part 1 without making use of the Euclidean Parallel Postulate? I know that d(A,B)+d(B,D)= d(A,D...
2022-07-25 16:42:59

Prove without Parallel Postulate

Let $x$ and $y$ be parallel lines where $x\neq y$. How do I prove that $y$ is in one of the $1/2$ planes , let's call it $H$ of $x$ ? How to prove that one of $1/2$ planes of $y$ is contained in $H$. Any suggestions or comments are welcome.
2022-07-25 16:41:06