SCSPARTAN CODEMATH · Basic Knowledge Survival Reference online

SPARTAN CODE: MATH / Reference 001

Basic knowledge
is survival equipment.

Learn the math behind measuring, building, saving, moving, and fixing things. Start with a job you know. Then see how the 1899 book taught the same idea.

Open field calculators ↘Quick reference kitRead the complete original
21knowledge chapters
49interactive models
84answered exercises
370source pages mapped
FIELD SYSTEM / 0011899 → 2026
CORE CAPABILITYPractical
Mathematics

Read the conditions. Build the model. Check the answer.

01–05
MeasureUnits, arithmetic, precision, proportion
06–10
NavigateScale, coordinates, graphs, logarithms
11–16
BuildGeometry, area, volume, material estimates
17–21
MoveMechanics, energy, machines, formulas

Basic Knowledge Survival

A field manual for thinking clearly.

The book starts with units. Then it moves through numbers, shapes, motion, and formulas. Each chapter now begins with a job you may do today. A short note shows where that idea appears in Castle’s 1899 book.

ONE SIMPLE PATH

Try a real job. See the math. Find the same idea in the old book.

  1. 01
    Measurement, Units, and PrecisionMeasure · Castle pp. 1–6
  2. 02
    Area, Volume, and DensityMeasure · Castle pp. 7–21
  3. 03
    Time, Angle, and RotationMeasure · Castle pp. 22–38
  4. 04
    Arithmetic as a Working LanguageMeasure · Castle pp. 39–58
  5. 05
    Ratio, Proportion, and PercentageMeasure · Castle pp. 59–75
  6. 06
    Algebra as a MachineNavigate · Castle pp. 76–95
  7. 07
    Approximation and ErrorNavigate · Castle pp. 96–109
  8. 08
    Unknowns in BalanceNavigate · Castle pp. 110–127
  9. 09
    Graphs as Measuring InstrumentsNavigate · Castle pp. 128–141
  10. 10
    Logarithms: Multiplication by AdditionNavigate · Castle pp. 142–157
  11. 11
    Triangles in the FieldBuild · Castle pp. 158–177
  12. 12
    The Slide Rule and the Shape of ComputationBuild · Castle pp. 178–188
  13. 13
    Sequences, Growth, and FinanceBuild · Castle pp. 189–199
  14. 14
    Projection: Three Dimensions on TwoBuild · Castle pp. 200–227
  15. 15
    Area by StructureBuild · Castle pp. 228–250
  16. 16
    Area from SamplesBuild · Castle pp. 251–263
  17. 17
    Volume by DecompositionMove · Castle pp. 264–285
  18. 18
    Motion, Work, and EnergyMove · Castle pp. 286–298
  19. 19
    Forces, Vectors, and StructuresMove · Castle pp. 299–326
  20. 20
    Curves, Stress, and Material ResponseMove · Castle pp. 327–353
  21. 21
    Formulae as Executable ModelsMove · Castle pp. 354–370

The complete 1899 source

Every page. Every chapter.
Nothing left behind.

The full public-domain text sits beside the rebuilt edition. Read all 21 OCR chapter transcripts online, move chapter by chapter, or open the complete 387-page archival scan when the page itself matters.

Open the original text →View archival scan
Public-domain source · text preserves original wording · OCR may contain scan artifacts

SPARTAN CODE: MATH / Field tools

Forty-seven math tools.
Each starts with real life.

Pick a task you know. Put in your numbers. The answer changes right away. Each tool also points back to the chapter and pages that teach the original idea.

A one-minute tour

Choose a job.
Change a number.
Use the answer.

Each example is already filled in. Open one, look at the first answer, then change one measurement to match your job.

Some tools link to a public patent record that shows the math at work in industry. A public record does not mean the invention is free to copy.
  1. 01

    Paint a wall

    How much paint should I buy?

    A 6.8 m wall with a pointed top, openings, and two coats needs about 3.25 L.

  2. 02

    Make a workbench

    How many top boards do I need?

    A 180 × 75 cm top made with 15 cm boards needs five boards across.

  3. 03

    Drain a water tank

    How long will gravity take?

    A 1.2 m round tank with 1 m of water and a 25 mm outlet takes about 28 minutes.

  4. 04

    Power several devices

    How long will the battery last?

    A 1,000 Wh battery running three 10 W lights and one 45 W laptop may last about 10.2 hours.

Power check / AC versus DC

The labels look alike.
The math can change.

A battery sends DC in one direction. An outlet sends AC back and forth. Start with volts and amps, then check the kind of power and the load.

DC or a heaterP = V × I

For a simple DC load, multiply volts by amps. A simple AC heater uses nearly the same step.

Single-phase AC motorP = V × I × PF

Motors can pull current that does not all become useful work. Power factor, or PF, adjusts the real watts.

Three-phase ACP = √3 × V × I × PF

Many shops use three-phase power. Use line voltage, line current, and this formula for a balanced load.

Why VA still mattersVA = V × I

W tells how much real work is done. VA tells how much electrical load the wires and equipment carry.

Use equipment nameplate values. Ask a qualified electrician before sizing wires, breakers, motors, or shop service.
Everyday starting points

Choose a real job. We will show the math behind it.

Today → 1899 · Chapter 01 · Castle pp. 1–6

Measurement Bench

Measure a board in inches. Then change the length to millimetres.

Live model
Use it today

Measure a board in inches. Then change the length to millimetres.

From the 1899 book

Castle starts with rulers, inches, and metres. We use the same unit change with phone scans and modern tools.

Read Chapter 1 →
Modern industry exampleLaser distance measurement device

A phone-linked laser tool measures a building, calculates material needs, and helps order the right amount.

Read public patent US11187803B1 ↗
Put in your numbers
Metric length190.5mm
Metric uncertainty0.254mm
Relative uncertainty0.133%
Modelmillimetres = inches × 25.4

The length is 190.50 mm. The ruler may be off by 0.25 mm.

Book + digital edition

One reference.
Three ways to use it.

The 6×9 print edition is in publisher review. A reflowable EPUB is the next publishing format, while the website and native apps carry the interactive layer that a static ebook cannot.

See the ebook production plan

Measuring + calculating devices

Choose the instrument
before trusting the number.

Browse a manufacturer-neutral directory of common measuring, layout, electrical, environmental, precision, and handheld calculating tools.

Open the field gear guide

One SPARTAN CODE library

Story carries the code.
Reference carries the method.

RED, BLUE, and WHITE remain the narrative sequence. MATH is Reference 001: a practical knowledge layer for every book and app in the system.

BOOK IRED

Narrative sequence

BOOK IIBLUE

Narrative sequence

BOOK IIIWHITE

Narrative sequence

REFERENCE 001MATH

Basic Knowledge Survival

One reference / every platform

Keep the knowledge with you.

The production website is the canonical home. Native iOS and Android editions keep all 49 interactive models available offline, with no account, ads, analytics, or tracking.

WEBLive reference

Complete source text, field index, and 49 interactive models in any modern browser.

Available here
iOSNative field app

SwiftUI companion with the complete model catalog stored on-device.

Build verification
ANDROIDNative field app

Jetpack Compose companion built for offline use from Android 8 onward.

Build verification

Operational protocol

Use the tool.
Keep the judgment.

Every result is an estimate until it is checked against the conditions in front of you.

01

Observe

Identify what is known, what must be measured, and which units are in use.

02

Model

Choose the simplest defensible relationship and make assumptions visible.

03

Verify

Check scale, units, limits, and whether the answer makes physical sense.

04

Record

Keep the inputs and method so the decision can be repeated or corrected.