Mathematics · Linear Algebra

Anisotropic Plane Area Scale second principal length scale Solver

Rearrange the anisotropic plane area scale relationship and solve for second principal length scale.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
second principal length scale7
Reconstructed area scale factor21

Calculation steps

  1. Use b=c/a with area scale factor=21 and first principal length scale=3.
  2. second principal length scale=7.
  3. Substitution into c=ab reconstructs 21.

Understand Anisotropic Plane Area Scale: solve second principal length scale

One idea, three depths

Choose how deeply to explain Anisotropic Plane Area Scale: solve second principal length scale

Anisotropic Plane Area Scale: solve second principal length scale: Rearrange the anisotropic plane area scale relationship and solve for second principal length scale.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Anisotropic Plane Area Scale: solve second principal length scale to answer this question: rearrange the anisotropic plane area scale relationship and solve for second principal length scale? Enter area scale factor and first principal length scale; the calculator shows second principal length scale. For example: first principal length scale=3 and second principal length scale=7 produce area scale factor=21. The answer tells you second principal length scale.

Age 15Explain it to a 15-year-oldConnect it to the formula

Independent principal length scales multiply to give the oriented area's magnitude scale. This page isolates second principal length scale and verifies it in the original relationship. The rule is b=c/a. Its input values are area scale factor, first principal length scale, and the main result is second principal length scale. For example: first principal length scale=3 and second principal length scale=7 produce area scale factor=21.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated anisotropic plane area scale: solve second principal length scale relation over the valid real-number domain stated below. The implemented relation is b=c/a, evaluated from area scale factor, first principal length scale to produce second principal length scale. Independent principal length scales multiply to give the oriented area's magnitude scale. This page isolates second principal length scale and verifies it in the original relationship. A sign or rotation convention may be needed for a full signed Jacobian determinant.

Inputs and valid domain

  • area scale factor must be a finite real number.
  • first principal length scale must be a finite real number.

Important boundary: A sign or rotation convention may be needed for a full signed Jacobian determinant.

The formula

b=c/a

How the calculator works through it

It substitutes area scale factor, first principal length scale into the formula and exposes every numerical step above. The main output is second principal length scale, accompanied by Reconstructed area scale factor.

Read the result correctly

The second principal length scale is the direct answer to “rearrange the anisotropic plane area scale relationship and solve for second principal length scale.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

first principal length scale=3 and second principal length scale=7 produce area scale factor=21.

Where this model stops being reliable

A sign or rotation convention may be needed for a full signed Jacobian determinant.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Anisotropic Plane Area Scale: solve second principal length scale works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Anisotropic Plane Area Scale: solve second principal length scale uses b=c/a. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

  • Vectors and components

    Component notation helps you follow how Anisotropic Plane Area Scale: solve second principal length scale combines directional or indexed values.

    Review this foundation about 6 min

Optional enrichment

  • Matrices and linear transformations

    Matrices place Anisotropic Plane Area Scale: solve second principal length scale inside the wider language of linear systems and transformations.

    Review this foundation about 7 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read area scale factor, first principal length scale.
  2. Evaluate the principal relationship: b=c/a.
  3. Return second principal length scale and check the domain conditions described above.
Python
            from math import *

def anisotropic_plane_area_scale_solve_b(c, a) -> float:
    return (c / a)

assert abs(anisotropic_plane_area_scale_solve_b(21, 3) - 7) < 1e-6 * max(1.0, abs(7))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double anisotropic_plane_area_scale_solve_b(double c, double a) {
    return (c / a);
}

int main(void) {
    const double expected = 7;
    const double actual = anisotropic_plane_area_scale_solve_b(21, 3);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double anisotropic_plane_area_scale_solve_b(double c, double a) {
    return (c / a);
}

int main() {
    constexpr double expected = 7;
    const double actual = anisotropic_plane_area_scale_solve_b(21, 3);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double anisotropic_plane_area_scale_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global anisotropic_plane_area_scale_solve_b
section .text

anisotropic_plane_area_scale_solve_b:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    divsd xmm0, [rbp-16]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = anisotropic_plane_area_scale_solve_b(c, a)
    result = (c / a);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[c_, a_] := (c / a);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Algebra and Trigonometry 2e

Read the related free OpenStax mathematics chapters
Cite this book
APA 7
Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
MLA 9
Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
Chicago author-date
Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Anisotropic Plane Area Scale second principal length scale Solver. MW SysArc Tools. https://math.mwsysarc.com/linear-algebra/anisotropic-plane-area-scale-second-principal-length-scale-solver

MLA 9

MW SysArc. “Anisotropic Plane Area Scale second principal length scale Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/linear-algebra/anisotropic-plane-area-scale-second-principal-length-scale-solver. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Anisotropic Plane Area Scale second principal length scale Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/linear-algebra/anisotropic-plane-area-scale-second-principal-length-scale-solver.

Harvard

MW SysArc (2026) ‘Anisotropic Plane Area Scale second principal length scale Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/linear-algebra/anisotropic-plane-area-scale-second-principal-length-scale-solver (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_anisotropic_plane_area_scale_solve_b_2026,
  author = {{MW SysArc}},
  title = {Anisotropic Plane Area Scale second principal length scale Solver},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/linear-algebra/anisotropic-plane-area-scale-second-principal-length-scale-solver},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Anisotropic Plane Area Scale second principal length scale Solver
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/linear-algebra/anisotropic-plane-area-scale-second-principal-length-scale-solver
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Anisotropic Plane Area Scale: solve second principal length scale do?

Rearrange the anisotropic plane area scale relationship and solve for second principal length scale.

How does the Anisotropic Plane Area Scale: solve second principal length scale work?

The calculator applies b=c/a. Independent principal length scales multiply to give the oriented area's magnitude scale. This page isolates second principal length scale and verifies it in the original relationship.

What can I learn from the Anisotropic Plane Area Scale: solve second principal length scale?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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