# What is Interior: Definition and 149 Discussions

Interior design is the art and science of enhancing the interior of a building to achieve a healthier and more aesthetically pleasing environment for the people using the space. An interior designer is someone who plans, researches, coordinates, and manages such enhancement projects. Interior design is a multifaceted profession that includes conceptual development, space planning, site inspections, programming, research, communicating with the stakeholders of a project, construction management, and execution of the design.

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1. ### The interior design of the central trunk of a ring spaceship

For all the attention we‘ve paid to ring habitats, we haven’t talked that much about the interior design of the central trunk yet, around which the rings rotate. Just having one big hollow ship trunk, about 100 metre in diameter, would be a lot of wasted space. It would also be too easy for...
2. ### I Calculating the thermal coefficient between the insulated interior of a telescope instrument package and the cold ambient air outside

I've built an insulated chamber to protect a sensitive instrument at freeze temperatures in the winter. The instrument is mounted on a telescope, so the heat inside the chamber will slowly dissipate in the ambient. A digital PID thermostat is used to keep the temperature at a safeguard level...
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### Area of interior triangle of pyramid normal to a side length

This isn't homework, but I figured it's fine if I make it a HW problem and post here (if not, please let me know). Let ##z^*=0## be the vertex of the pyramid, and let ##z^*## run the altitude. It's easy to show the area of the base normal to the altitude is ##A = 4 \left.z^*\right.^2...
4. ### I Discussing Interior Schwarzschild Proper Lengths & Gaussian Curvature

I'd love have a little discussion about the Interior Schwarzschild Solution. Here's a diagram I slapped together to illustrate the key points. (I assume everyone reading this familiar with embedding diagrams, and using an axis to 'project' a value, in this case the spatial z-axis is replaced by...
5. ### I Closure & Interior as Dual Notions .... Proving Willard Theorem 3.11 ...

I am reading Stephen Willard: General Topology ... ... and am studying Chapter 2: Topological Spaces and am currently focused on Section 3: Fundamental Concepts ... ... I need help in order to prove Theorem 3.11 Part 1-a using the duality relations between closure and interior ... ..The...
6. ### I Interior and Closure in a Topological Space .... .... remark by Willard

I am reading Stephen Willard: General Topology ... ... and am currently focused on Chapter 2: Topological Spaces and am currently focused on Section 3: Fundamental Concepts ... ... I need help in order to fully understand a result or formula given by Willard concerning a link between...
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### How do we show that the interior of a Faraday cage is an equipotential?

It is possible to show via Gauss' law that the the net flux through a surface within the Faraday cage must be zero, however this is not a sufficient condition for the electric field to be zero. For the electric field to be zero in the interior of the cage, all points within the cage must be at...
8. ### Construction Allowing for drywall when framing an interior room

What are the best methods for framing the locations where a new interior room meets the wall and ceilling of an existing interior room? I'll be adding a small closet to a room of a house. The rectangular closet will have 3 new walls and use one existing interior wall. The new walls will be...
9. ### MHB Sum of the measures of the interior angles of a heptagon

PLEASE HELP1.What is the sum of the measures of the interior angles of a heptagon? A. 1260∘ B. 2520∘ C. 900∘ D. 1800∘ my answer is C 5.If the sum of the interior angle measures of a polygon is 3600∘, how many sides does the polygon have? A. 22 sides B. 20 sides C. 18 sides D. 10 sides MY...
10. ### MHB Finding border points and then interior points

I am working on a classical real analysis problem as follow: The answers from solution manual are respectively $int (A) = \emptyset$ and $bd (A) = \{0\} \cup \{ \frac{1}{n} | n \in \mathbb N \}$. And here are my textbook's definition of interior point and border point: And then there is...
11. ### A Interior volume of a black hole

This paper by Christodolou and Rovelli discusses how to define the interior volume of a black hole: https://arxiv.org/abs/1411.2854 I'll try to condense their basic argument into a (heuristic) form that makes it easier to raise the issues I want to raise. The basic idea is to start with the...
12. ### Interior of the set of "finite" sequences

Homework Statement Identify the boundary ##\partial c_{00}## in ##\ell^p##, for each ##p\in[1,\infty]## Homework Equations The interior of ##S## is ##\operatorname{int}(S) = \{a\in S \mid \exists \delta > 0 \text{ such that } B_\delta (a) \subseteq S\}##. ##\partial S = \bar{S}\setminus...
13. ### MHB Can we find the interior of the given curve using Green's theorem?

Hello! (Wave) Using Green's theorem, I want to compute the integral $$\oint_C ydx+xdy$$ where $C$ has the parametric representation $r(t)=2 \cos^3 t i+ 2 \sin^3 t j, (0 \leq t \leq 2 \pi)$. Using Green's theorem, we get that $\oint_C ydx+xdy=\iint_U (1-1)dxdy=0$. I am wondering if we could...
14. ### Are my definitions of interior and closure correct?

Homework Statement Define the interior A◦ and the closure A¯ of a subset of X. Show that x ∈ A◦ if and only if there exists ε > 0 such that B(x,ε) ⊂ A.The Attempt at a Solution [/B]
15. ### I How to describe the Sun's interior?

My question to you is this... Can the interior of the Sun be described as an ideal gas? From my knowledge, to describe a body of gas as an ideal gas, the separation between the particles must be much greater than the size of the actual particles. How could one justify whether the Sun fits this?
16. ### I Proof that p is interior if p is not limit of complement

Hello PF, I am searching for a proof that I couldn't find on the internet. Theorem: E in X a metric space. p in E. p is an interior point of E if and only if p is not a limit point of (E complement)' Sorry for notations but I have no idea how to insert Latex here.
17. ### Total interior and exterior charge of a hollow sphere?

Homework Statement A hollow conducting sphere has inner radius R and outer radius 1.5R. A +40nC point charge is placed at the center. What is the total charge on the interior and exterior walls of the sphere? R=10cm Homework Equations Gauss's Law σ = Qenc/A The Attempt at a Solution I'm not...
18. ### Interior and Exterior Angle of a Polygon: Formula not working

Homework Statement How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle? Homework Equations Interior angle of a polygon: ((n-2) * 180)/n Exterior angle of a polygon: (360)/n The Attempt at a Solution ((n-2) * 180)/n = 8 *...
19. ### I Can we experimentally understand the interior of a star?

I have heard that whatever we know about stars experimentally is through only what we can see from its surface since the light from the interior is "hidden." However, when we look at the spectrum of a star, we do see absorption lines for heavy elements. I think the reason why that is is because...
20. ### Effusing gas onto the interior of an evacuated sphere

Homework Statement A gas effuses into a vacuum though a small hole of area A. Show that if the particles effused into an evacuated sphere and the particles condensed where they collided that there would be a uniform coating. (7.6 of Blundell and Blundell) Homework Equations Angular...
21. ### MHB A cube with 9 interior points: Show that at least two of them are less than √(3)/2 apart.

There are $9$ points in the interior of a cube of side $1$. a) Show that at least two of them are less than $\frac{1}{2}\sqrt{3}$ apart. b) Can $\frac{1}{2}\sqrt{3}$ be replaced by a smaller number?
22. ### I Corollary to the Interior Extremum Theorem .... ....

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 6: Differentiation ... I need help in fully understanding the corollary to Theorem 6.2.1 ... Theorem 6.2.1 and its corollary ... ... read as follows: I am...
23. ### MHB Understanding Corollary 6.2.2 of B&S Theorem 6.2.1

I am reading "Introduction to Real Analysis" (Fourth Edition) by Robert G Bartle and Donald R Sherbert ... I am focused on Chapter 6: Differentiation ... I need help in fully understanding the corollary to Theorem 6.2.1 ...Theorem 6.2.1 and its corollary ... ... read as follows: Can someone...
24. ### I Interior Product: Definition & Understanding

Hello! The interior product is defined as ##i_X:\Omega^r(M)\to \Omega^{r-1}(M)##, with X being a vector on the manifold and ##\Omega^r(M)## the vector space of r-form at a point p on the manifold. Now for ##\omega \in \Omega^r(M) ## we have ##i_X\omega(X_1, ... X_{r-1}) = \omega (X,X_1, ...
25. ### I Rotating Black Holes: A Century of Discovery & Beyond

Schwarzschild black holes were discovered over 100 years ago, in 1915. Quite soon, in a couple years (by 1916...1918), charged Reissner-Nordström holes were discovered. Yet rotating black holes were only discovered by Kerr in 1963 - 48 years after Schwarzschild holes. Why? What was known about...
26. ### A Interior Schwarzschild Metric: Pressure Dependence

I'm looking influence of pressure on the general interior Schwarzschild metric (see for example the book by Weinberg, eq. 11.1.11 and 11.1.16. The radial component of the metric (usually called A(r)) depends only on the mass included up to radius r A(r) = \left(1-\frac{ 2G M(r)}{r}\right)^{-1}...
27. P

### I Why can't the interior of a black hole be empty?

Can someone explain to me why there must be a real/meaningful space inside of a black hole? I have been autodidactically working on understanding the mathematical concepts that general relativity is based on, so I've never had anyone to ask questions to (until it occurred to me to find a forum...
28. J

### Directional Grooves on the Interior of Pipes

Hey everyone! My name is Jing and I am participating in a one month summer program called SHAD where 800 high school students across Canada come together to try and solve some of the world's most multi-dimensional problems. One of the aspects of this program is the Entrepreneurial Project, where...
29. ### I Deriving Schwarzschild Interior Boundary Conditions

I've been playing around with Maxima and it's ctensor library for tensor manipulation. I decided to have a crack at deriving Schwarzschild's solution for the interior of a constant-density sphere. I've managed to derive a static, spherically symmetric solution, but am struggling a bit with the...
30. ### Writing: Input Wanted Design of large rotating asteroid interior space

Hi. I'm working on a science fiction story about colonization of the solar system. Asteroid way stations are an important part of the story. I want to construct a realistic scenario about how we could convert the Eros asteroid into a shuttling habitat in it's current orbit (or something close...
31. ### I Exploring the Interior of a Black Hole: Space-Like Separation Beyond the Horizon

Forgetting about the singularity for the moment, is the interior of a black hole a space-like region? That is, are any two events that occcur past the black hole horizon space-like separated? Thanks in advance.
32. ### I Interior and closure in non-Euclidean topology

Hello everyone, I was wondering if someone could assist me with the following problem: Let T be the topology on R generated by the topological basis B: B = {{0}, (a,b], [c,d)} a < b </ 0 0 </ c < d Compute the interior and closure of the set A: A = (−3, −2] ∪ (−1, 0) ∪ (0, 1) ∪ (2, 3) I...
33. ### An interior Dirichlet problem for a circle

Homework Statement $$\bigtriangledown^2=0 for : 0<r<1 \\ BC : u(1,\Theta)= sin(\Theta), 0<\Theta<\pi \\ u(1,\Theta)= 0, pi<\Theta<2\pi \\$$ Basically its an interior dirichlet problem for a circle. [/B]Homework EquationsThe Attempt at a Solution The answer is supposed to be U(r,\Theta) =...
34. ### A Interior products, exterior derivatives and one forms

If ##\bf{v}## is a vector and ##\alpha## is a ##p##-form, their interior product ##(p-1)##-form ##i_{\bf{v}}\alpha## is defined...
35. ### Processor Interior Schematics?

Does anybody know where to find schematics of the interior of modern processors for lithography? Not brand new, as far back as 32nm nodes? Or where to begin with this search? Thank
36. ### Exploring Earth's Interior with Seismic Tomography and Weather Bombs

This could open a new frontier on seismic study of the Earth's interior. http://www.bbc.com/news/science-environment-37177575 From, http://science.sciencemag.org/content/353/6302/919 Seismic tomography is like an x-ray of Earth's interior, except that it uses earthquakes for the illumination...
37. ### Metric Spaces: Interior of a Set

Homework Statement Let ##(X,d)## be some metric space, and let ##A## be some subset of the metric space. The interior of the set ##A##, denoted as ##int A##, is defined to be ##\bigcup_{\alpha \in I} G_\alpha##, where ##G_\alpha \subseteq A## is open in ##X## for all ##\alpha \in I##. The...
38. ### Simplifying Exterior Angles in a Polygon

Homework Statement Homework Equations sum interior angles (n-2)*180 angles of a quadrilateral: a+b+c=d = 360 [/B] The Attempt at a Solution What do you do with the exterior angle? 80+130+a+x=360
39. ### I The cold interior of the Sun seen in a sun spot

The sun we see has a measured surface temperature of 5800K. This is the temperature of the photosphere , a glowing layer of plasma radiating energy from the sun. But when there is a hole in this layer and we look deeper into the interior the temperature drops to 3800K. How can this possibly be...
40. ### Is greenhouse interior much cooler if reflective inside?

Let's assume typical 10' X 20' greenhouse for growing veggies is empty and is all exposed concrete black floor with solid black (opaque) insulated knee high walls all around. The rest of it is glass sides and roof. Also, assume reflective radiant barrier was hung on those knee walls inside...
41. ### I Can "extremal" strain tensors be in the interior of the body

I am new to elastic theory. I have a question about elasticity. We assume we have a body with no internal forces. Surface forces are applied on the border. Can we leave the elastic domain (reach the yield surface) in an interior point without leaving the elastic domain on the boundary? If no...
42. ### I Interior product with differential forms

Hi. I'm trying to self-study differential geometry and have come across interior products of vectors and differential forms. I will use brackets to show the interior product and I would just like to check I am understanding something correctly. Do I need to manipulate the differential form to...
43. ### Why Does the Set {1/n : n ∈ ℕ} Have an Empty Interior?

Hi All, A simple question but one for which I cannot seem to get the intuition. 1. Homework Statement Find the interior point of {1/n : n ∈ ℕ}. Homework Equations N/A The Attempt at a Solution Let S = {1/n : n ∈ ℕ}, where S ⊆ℝ x is an interior point if ∃N(x ; ε), N(x ; ε) ⊆ S. My...
44. ### Ansoft Maxwell -- shaping an interior electric motor rotor

For shaping an interior PMSM rotor from top figure to as in bottom fig, I made an equation based curve, united with another curve , made a surface using coverline and united that shape with my rotor. When validated it showed band and rotor intersecting and I adjusted the band - DiaGap. Then...
45. ### MHB Given 3 sides of a triangle, compute interior angles and area

Just attempted another exam question. Would you mind correcting me if I am wrong? The question is A triangle ABC has sides of length AB= 3.5 m, BC = 5.1 m and AC = 4.2m. a) Calculate the size of the angle B and the size of the angle C, in degrees correct to 1 decimal place, in each case...
46. ### Crossing the Event Horizon: Observing a Massive Black Hole

A number of recent threads have discussed what happens when an observer falling into a massive black hole passes the event horizon. What I would like to know is this. For a massive BH of mass M, Schwartzchild Radius Rs, how long would it take for such an observer (who, presumably crosses the...
47. ### Percentage change in interior volume

Homework Statement Deep sea fish experience a tremendous amount of atmospheric pressure. When you are at a depth of 2000 m in the sea, the pressure that you will experience is about 200 times atmospheric pressure (1atm=1.0×105N/m2)which you will experience on land. If you are lowering a...
48. ### MHB The rectangle has an empty interior

Hey! :o Show that the measure of a rectangle is zero if and only if it has an empty interior. When a rectangle has an empty interior, does this mean that the length of the sides of the rectangle are equal to zero?? (Wondering)
49. ### Topology on a set ##X## (find interior, closure and boundary of sets)

Homework Statement . Let ##X## be a nonempty set and let ##x_0 \in X##. (a) ##\{U \in \mathcal P(X) : x_0 \in U\} \cup \{\emptyset\}## is a topology on ##X##. (b) ##\{U \in \mathcal P(X) : x_0 \not \in U\} \cup \{X\}## is a topology on ##X##. Describe the interior, the closure and the...
50. ### How can the interior product be visualized using a concrete example?

In Nakahara's book, the interior product is defined like this : i_{x} \omega = \frac{1}{r!} \sum\limits_{s=1}^r X^{\mu_{s}} \omega_{\mu_{1}...\mu_{s}...\mu_{r}}(-1)^{s-1}dx^{\mu_{1}} \wedge ...\wedge dx^{u_{s}} \wedge...\wedge dx^{\mu_{r}} Can someone give me please a concret example of...