The MiniApps are spread over 36 Domains (some
MiniApps appear in multiple Domains). Each MiniApp is a standalone
computation which generates one or more values, a table, or a report,
each with the input, relevant equation, and output clearly
presented. Tap the [
MiniApps] tab to visit
a list of the Domains, then tap any entry to see the MiniApps in that
Domain. Or, tap [
MiniApps] → {
All MiniApps} for a list of all the MiniApps.
MiniApps are popular because each covers a single task, and they
minimize the amount of typing needed to get to the answer you
want. Among the Domains are:
• Health &
Fitness, with nine MiniApps, including Calories Burned, Body Mass
Index, Aerobic Points Earned, and Heart Rate.
•
Dollars & Sense, with 12 MiniApps, including Payoff Strategies,
Refinance, IRA futures, Bill Split and Present/Future Values.
• Math, with 133 MiniApps, including a wide range of
simple (to not so simple) computational tools. All the usual suspects
are available, and also simple MiniApps for integration, complex
arithmetic, intersecting shapes, solving quadratic, cubic and quartic
equations, summations, some matrix and vector operations, ...
• Integer Computations, with 22 MiniApps, including
modulo computations, various base representations, bit count, factoring,
summations, and Fibonacci and other series, ...
•
Solvers, with 44 MiniApps, including equation solvers, dot and cross
products, distance computations, LCM, GCD, integration, Amdahl's Law,
distance to the horizon, ...
• Physics, with 28
MiniApps, including Ohm's Law, e = mc², Potential and Kinetic
Energy, Capacitance and Resistance, Power and Work, ...
• Toss Ups, with Coin Flip, Dice Toss, Rock-Paper-Scissors,
Sheldon Cooper's Rock-Paper-Scissors-Lizard-Spock, and the very
un-intuitive Three Doors.
• And 29 other
Domains
Here is a simple Solver MiniApp for a common homework problem:
Find the
values of
x,
y, and
z for these three equations.
- 3x + 5y + 2z = 22
- x + 2y + 4z = –23
- ½x – y – z = 9
The [
Crunch] tab delivers
the full power of the app to the user's fingertips. Users enter
expressions or equations into the box. On-the-fly error detection
catches most typos instantly. When the first two characters of a
Function or Constant are entered, a list of expansion candidates is
automatically generated. When equation entry is complete, the user
taps the [Submit] button.
CrunchJr then parses the
input (with full error checking and diagnostic messages). If there
are any variables, it asks for one or more values for each, then
calculates the results and presents them in a tabular form for easy
review. The output generated shows the input equation and values
for the variables (if any). The result variable values are
automatically saved for reference and use in this or future sessions.
There are 300+ Functions and 200+ Constants that can be used as
part of the input equation. Functions and Constants are discussed
briefly in the next section, or tap [
Inputs]
→ {
Functions} or → {
Constants} for full lists. Most of the Functions
return a single value and can be used anywhere in an equation that a
number or a Constant can be used. But, about 130 of the Functions
are special purpose (they return text or a table of results), and thus
cannot be used with other terms in an equation (e.g., MatrixInv(),
EasterDate(), ComplexDiv(), PayoffBiweekly()). Here are two
samples, a simple mileage computation and a more complex,
engineering-style computation.
1)
Weekly commute is 423 miles, and a fill-up is between 13.5 and
15.5 gallons. Tap the [
Crunch] tab, then
enter the simple equation
mpg = 423/gals into the
box and tap [Submit], then enter nine values for
gals. Here
is what the output would be:
2) A more complex example with two
variables:
ρ = β + Cos(x+√x+πx²/β )
The
2 variables are
beta and
x.
Tap the [
Crunch] tab, then enter the equation
rho = beta+cos(x+sqrt(x+pi*x^2/beta))
As you type, the bottom panel (Screen 1 below) gives you
on-the-fly information about what you've typed so far. In this
case, it shows that you are in the middle of the argument for the
Sqrt function, you've also used one other function (Cos) and one
Constant (PI), and 3 variables (
rho,
beta, and
x
(twice)). After entering the complete equation, hit the [Submit]
button. Oops, you left off a "
)" – go back and add
the
) and hit [Submit] again. Screen 3 below appears and
asks you for values.
Enter 3 values for
beta (.45, .17, .33)
and 3 values for
x (.22, .839, 1.61) and tap the [Submit] button,
and your result appears on Screen 4.
The nine values for
rho are automatically saved for
later review or use as input. For this example, the
Show
OpCount/Time toggle has been set to ON (tap [
Info] → {
Settings} to get
to the options and toggles). The
OpCount is an approximate
count of primitive operations (+, –, ×, /, shift, compare)
for the computation itself (but not those for rendering the results into
human-readable format). The original equation and the values for
the input variables are also saved, and may be recalled from the History
later. Equations from the History may also be redone with new
values for the variables. Tap [
Inputs]
→ {
History} to get to the history list.
The [
Inputs] tab provides
eight entries which support Crunch expressions
| (Favorite
Functions) | | User-Defined Functions |
|---|
| Functions | | Most Recently Used |
|---|
| Constants | | Most Frequently Used |
|---|
| Variables (Store) | | History |
|---|
• (Favorite
Functions): Users can get rapid access to a set of their favorite
functions by tapping the [
+Fav] button for
each
• Functions: Lists the 300+
functions. By tapping an entry, a full description of what it does
and what its arguments are, as well as buttons to automatically place
the function name in the [Submit] box.
•
Constants: Lists the 200+ constants. By tapping an entry, its
value and description are displayed, as well as buttons to automatically
place the constant in the [Submit] box.
• Variables
(Store): Lists all the entries retained in the Store. By
tapping an entry, the variable and its values are displayed.
• User-Defined Functions: Provides the mechanisms to
create and display user-defined functions. These functions can be
used anywhere a regular function can appear. When an equation with
a user-defined function is used, its definition is displayed above the
results. Here is a sample:
scos(a,b) → a*sin(b)+b*cos(a)
Use it
like any other function, e.q.,
scos(.556,alpha)
• Most Recently Used: Lists the most recently used Functions
or Constants
• Most Frequently Used: Lists
the most frequently used Functions or Constants
• History: Lists all the equations which have been
entered. Any of them can be re-executed, with the original
variable values or a new set of values.
The [Search] tab provides a
simple, single keyword search capability over all the Functions,
Constants, and Screens. At the third character entered, it
displays pointers to the keyword hits. For example, metr
generates 10 hits (5 Functions, 4 Constants, 1 Screen), and mass
genrates 19 hits (9 Functions, 8 Constants, 2 Screens). Just tap
any entry to go to the information for that keyword. Note that
metr gets 10 hits, but etr gets no hits, because no
keywords start with etr. Also, the [Inputs] → {Functions} page
has a Functions-only keyword search, the [Inputs]
→ {Constants} page has a Constants-only
keyword search, and the [Info] → {All Screens} page has a Screens-only keyword
search.
The [
Info] tab provides
access to all the internal documentation and help files (including this
one), as well as an avenue to the Options & Toggles, the Contact Us
page, a Reset capability, the Pasteboard contents, and a list of all the
screens in alphabetical order for easy reference. Among the tables
and reports are several handy lookup tables (most very special-purpose,
some unusual, some esoteric), including:
| Greek Alphabet | |
ASCII Codes | |
Powers of 2 |
|---|
| Morse Code |
| Phonetic Alphabet |
| Powers of 10 |
|---|
| Metric Conversions | |
Keywords for C++,
C, Java, CrunchJr |
| English Letter
Frequency |
|---|
| Pythagorean Triads | |
Prime Numbers | |
Roman Numerals |
|---|
| HTML Symbols | |
Genetic Code | |
Chemical Symbols |
|---|
| Area Codes | |
Airport Codes | |
Periodic Table |
|---|
| URL Country Codes | |
Poker Distributions | |
Bridge Distributions |
|---|
| | | Math Trivia |
|---|
Each of these will likely have very infrequent use, but it may be
handy to have them nearby when needed. Click
here for a full list of the tables and reports.
| Solvers
|
|---|
| Quadratic, Cubic, Quartic
|
|---|
| Integration |
|
LCM, GCD |
|---|
| Distances |
|
Amdahl's Law |
|---|
| e = mc² |
|
Pythagorean |
|---|
| N Equations in N
Unknowns |
|---|
| . . . 33 more |
|---|
|
| Dollars
& Sense |
|---|
12 Payoff Stategies |
| IRA Profiles |
|
Refinance |
|---|
| Bill Split, Tips |
|
Mortgage Attrs |
|---|
| Mileage ($) Tracking |
|
Price Per |
|---|
| Effective, Nominal
Rates |
|---|
| Present, Future
Value |
|---|
|
| Health
& Fitness |
|---|
| Calories Burned (38
workouts) |
|---|
| Target HeartRates |
|
BMI |
|---|
| Heat Index |
|
Windchill |
|---|
| Race-Pace, -Time |
|
Fitness Tests |
|---|
| Aerobic Points Earned |
|---|
|
| Math
Stuff |
|---|
Trig (the 21 usual
suspects + 1) |
| Factoring |
|
Binomial(4) |
|---|
| Alternate Bases (2-36) |
|
Bit Count |
|---|
| Complex Arithmetic(12) |
|
Factorials |
|---|
| Normalize(3), Fibonacci,
Max, Min |
|---|
| Summations(11), Series(7),
Stats(5) |
|---|
| Cube Root, Mod,
Inverse Mod |
|---|
| Sqrt, Exp, Log,
Random(2) |
|---|
| . . . 72
more |
|---|
|
| Other
Categories, Etc |
|---|
| 250+ MiniApps |
|---|
| 150+ HelpFiles, Tables,
Reports |
|---|
| Physics(34) |
|
Matrix(13) |
|---|
| Geometry(73) |
|
Vector(14) |
|---|
| Group Data(36) |
|
Colors(4) |
|---|
| Statistics(5) |
|
Roots(8) |
|---|
| Temperatures(10) |
|
Dates(12) |
|---|
| Intersecting Shapes(14)
|
|---|
| . . . yada, yada, yada
|
|---|
|
| Miscellaneous |
|---|
Rock-Paper-Scissors-Lizard-Spock |
| Dice |
|
Easter Date |
|---|
| Three Doors |
|
Prime Numbers |
|---|
| Math Trivia |
|
Factorials |
|---|
| Roman Numerals |
|
Phonetic Alphabet |
|---|
| Periodic Table |
|
Chemical Elements |
|---|
| CrunchJr Tour |
|
Search |
|---|
| History Replay |
|
Auto-expansion |
|---|
| On-the-fly error
detection |
|---|
|
