Author: shiroe

Shopping for clearance and discounted items

This is a calculation for buying either "discounted items" or "sale items" while shopping.

So, how much is the discount, exactly?

Let's say you're shopping at a store right now.

Can I afford that discounted item within my budget??

Let's say you're out shopping right now.

Where can I return those plastic bottles I bought in bulk??

Let's say you just bought a bunch of plastic bottles that hold less than 1 liter (such as beverages).

How many minutes does it take to make that wish come true?

Reciting scripture, projecting affirmations into the future, emitting the power of words—the motivations for “reciting” are diverse.

How many minutes does it take to make that wish come true? (2)

Reciting a mantra 1,000 times to make a wish come true is a basic practice, but before you challenge yourself by saying, “Let’s try to do it in X minutes!” why not check what kind of pace that would entail?

Calculate the coordinates of the vertex of a quadratic function.

Calculate the x and y coordinates of the vertex of the graph of the quadratic function y = ax² + bx + c (where a is not zero).

We will perform calculations related to cubic curves.

We will perform calculations related to cubic curves.

We will simplify the quadratic function using the method of completing the square.

We will perform calculations related to quadratic functions.

Divide the cubic polynomial by the quadratic polynomial.

Divide the cubic polynomial by the quadratic polynomial.

Check the value of the discriminant D of the quadratic equation

The discriminant D of the quadratic formula.

Calculate the maximum and minimum values of a quadratic function.

Calculate the maximum and minimum values of a quadratic function.

Calculate the maximum and minimum values of a cubic curve.

Calculate the maximum and minimum values of a cubic curve.

Convert the fraction to a mixed fraction.

We will do some calculations involving fractions.

Perform arithmetic operations on fractions.

Perform arithmetic operations on fractions.

Determines whether the substitution is even or odd. (3 characters)

Determines whether the substitution is even or odd.

Determines whether the substitution is even or odd. (4 characters)

Determines whether the substitution is even or odd.

We will perform calculations related to systems of two linear equations.

We will perform calculations related to systems of two linear equations.

Let's expand the expression (cubic).

Let's expand the expression.

Let's expand the expression. (4th degree)

Calculate the expansion of the expression.

Let's expand the expression. (Quadratic)

Calculate the expansion of the expression.

We will work on calculations involving fractions. Part 2.

We will do some calculations involving fractions.

Calculate the common denominator for these fractions. (Both are linear.)

Let's find a common denominator for these fractions.

Checking the value of the discriminant D of a quadratic equation. Part 2.

Let's check the discriminant D of the quadratic equation.

We will calculate the weighted geometric mean.

We will calculate the weighted geometric mean.

We will perform calculations related to the rules for calculating square roots.

We will perform calculations related to the rules for calculating square roots.

Check the expression inside the radical. (Related to nth roots)

Check the number inside the square root.

Determines whether the substitution is even or odd. (5 characters)

Determines whether the substitution is even or odd.

Calculate the partial fraction expansion. (3-term)

Calculate the partial fraction expansion.

Let's expand the expression. (5th degree)

Calculate the expansion of the expression.

Expand the expression. (The inverse of cross-factoring)

Let's expand the expression.

Calculate the partial fraction expansion.

Calculate the partial fraction expansion.

Calculate the partial fraction expansion (two-term)

Calculate the partial fraction expansion.

Calculate the factoring into partial fractions. (Numerator and denominator are quadratic expressions.)

Calculate the partial fraction expansion.

Calculate the partial fraction expansion. (4 terms)

Calculate the partial fraction expansion.

We will perform calculations involving fractions. Part 3. (Calculations involving powers of n)

We will do some calculations involving fractions.

Let's expand the expression. (6th degree)

Let's expand the expression.

Let's expand the expression. (quadratic × quadratic)

Let's expand the expression.

We will perform the calculation using the method of partial fractions (up to the 10th term).

Calculate the division of a polynomial using the synthetic division method.

Let's expand the expression. (Product of three linear expressions)

Calculate the expansion of the expression.

Let's expand the expression. (Four linear terms)

Let's expand the expression.

Calculate the number of positive divisors and their sum. (3 prime factors)

We will calculate the number of divisors and their sum.

We will examine the number of divisors and the sum of the divisors of a natural number.

We will examine the number of divisors of a natural number and the sum of those divisors.

Determines whether a substitution is even or odd. (6 characters)

Determines whether the substitution is even or odd.

Determines whether the substitution is even or odd. (7 characters)

Determines whether the substitution is even or odd.

Determines whether the substitution is even or odd. (8 characters)

Determines whether the substitution is even or odd.

Determines whether the substitution is even or odd. (9 characters)

Determines whether the substitution is even or odd.

Factoring into proper fractions

Let's do some Egyptian arithmetic.

List the divisors.

Let's examine the divisors of the natural number n.

Add and subtract fractions (up to 10)

We will calculate the addition and subtraction of multiple fractions.

Calculate the partial fraction expansion (Expansion/Arithmetic)

Calculate the partial fraction expansion.

We will perform calculations related to the sum of unit fractions.

We will perform calculations related to the sum of unit fractions.

Egyptian Calculus (Decomposition into unit fractions of a binomial)

Let's do some Egyptian arithmetic.

System of Equations [Product and Sum of x and y]

We will solve a system of equations.

Calculate the weighted average. (Up to 10 data points)

We will calculate the weighted average.

Determining a Circle from Three Points

A circle is defined by three points.

Egyptian Calculus (Decomposition into unit fractions of a trinomial)

Let's do some Egyptian arithmetic.

Calculate the weighted average. (Up to 30 data points)

We will calculate the weighted average.

Egyptian Calculus (Decomposition into unit fractions of a fourth-degree polynomial)

Let's do some Egyptian arithmetic.

Determining a Curve in Three Dimensions or Less Using Four Points

Determine a curve of degree three or less from four points.

Calculating the y-intercept (of a line, given a point and the slope)

Find the y-intercept of the line.

Calculating the Values of Polynomials (Up to the 10th Degree)

We will perform polynomial calculations.

Factoring (quadratic; integer range)

Let's factor this expression.

Composition of unit fractions (two-term). Inverse Egyptian calculation.

Find the denominator of a unit fraction that is the sum of two unit fractions.

Coefficients in the equation of a tangent line

Calculate the coefficients of the tangent line.

Calculating the coefficients of first and second derivatives

Calculate the coefficients of the derivative.

Calculate the singular transformation of natural numbers.

Let's perform the unit conversion calculation.

Find the number of digits in the natural number

Find the number of digits in a natural number n (in the decimal system).

Expand the expression (resulting in a quadratic expression)

Calculate the expansion of the expression.

Expand the expression (resulting in a cubic expression)

Calculate the expansion of the expression.

Calculate the value of the discriminant of a cubic equation.

Calculate the value of the discriminant of a cubic equation.

Equation of the tangent line to the irrational function

Calculate the tangent to the irrational function.

Divide the fourth-degree polynomial by the second-degree polynomial.

Divide the fourth-degree polynomial by the second-degree polynomial.

Applications of the Factor Theorem (Integer range; up to the 10th degree)

Let's work through a problem involving the Factor Theorem.

The number of multiples (for natural numbers up to n)

Calculate the number of multiples of a and b contained in the natural numbers from 1 to n.

The number of items that can or cannot be divided evenly

Given a range of consecutive natural numbers, determine whether each number is divisible by two distinct natural numbers, and summarize the results.

Divisible or not divisible (3 natural numbers)

For each natural number from n0 to n1, determine whether it is divisible by each of the three natural numbers a, b, and c, and count the number of such numbers.

Manipulating Fractional Functions

We will manipulate rational functions.

Number of Coprime Numbers

We will determine the number of natural numbers that are "mutually prime."

Search by Two "Remainders"

When a natural number n is greater than two distinct natural numbers a and b, we investigate the largest and smallest natural numbers such that, when divided by a, the remainder is Ra, and when divided by b, the remainder is Rb.

Finding Special Solutions to Diophantine Equations (Between x and y Intercepts; Integer Range)

We will search for particular solutions to indeterminate equations.

Finding Special Solutions to Diophantine Equations (Integer Range)

We will search for particular solutions to indeterminate equations.

Expand the expression. The product of two polynomials (up to the 5th degree)

Calculate the expansion of the expression.

Factoring (Cross-multiplication method) (Integer range)

We will perform cross-factoring.

Factoring. √ Available. Integer range

Let's do some factorization problems.

Using Logarithmic Formulas (Rearranging Equations; Finding Coefficients)

Let's perform algebraic manipulation on logarithmic expressions.

Using logarithmic formulas (converting coefficients to exponents of the argument)

Rewrite the logarithmic expression.

Here is a list of the common factors.

List the common divisors of two natural numbers, x and y.

List the common divisors. (For three natural numbers)

List the common divisors of the three natural numbers x, y, and z.

The length of the line segment cut off from the x-axis by the graph of a quadratic function

Calculate the length of the line segment cut off from the x-axis by the graph of a quadratic function.

Graphs of Fractional Functions (Linear/Linear)

Plot the graph of a rational function (linear/linear).

Manipulating Fractional Functions (Linear/Linear)

Calculate the transformation of a rational function.

Calculating Simplified Fractions (When the Numerator Is Unknown)

We will perform the inverse operation of simplifying fractions.

Calculating Simplified Fractions (When the Denominator Is Unknown)

We will perform the inverse operation of simplifying fractions.

Expansion of the expression (7th degree)

Calculate the expansion of the expression.

Expansion of the expression (8th degree)

Let's expand the expression.

Calculate the weighted average. (5 data sets)

We will calculate the weighted average.

Calculate the weighted average. (2 datasets)

We will calculate the weighted average.

Let's expand the expression. (nth power using the binomial theorem)

Let's expand the expression.

The Intersection Point of Direct and Inverse Proportional Equations

Calculate the point of intersection between a direct proportion and an inverse proportion.

Expansion of the expression (ninth degree)

Let's expand the expression.

Table of Values for Trigonometric Functions with Coefficients　

Outputs a table of numerical values for trigonometric functions with coefficients.

Table of Cosine Values

Outputs a table of cosine values with coefficients.

Rewriting Quadratic Functions Using the Completing the Square Method (2)

We will simplify the quadratic function using the method of completing the square.

Translation of Curves (Conic Sections)

We will calculate the translation of a conic section.

Greatest Common Divisor and Least Common Multiple

For two natural numbers A and B, this program outputs the results of the procedure for finding the least common multiple and the greatest common divisor.

Numeric Search for Inverse Factorials

We will calculate the inverse factorial.

Second-order square matrices, real symmetric matrices, Newton approximation

This is a numerical diagonalization method for real symmetric 2×2 matrices.

Multiply a 2D vector by a rotation matrix.

We will perform the calculation of multiplying a vector by a rotation matrix.

The product of three 2×2 matrices

Calculate the product of three 2x2 square matrices.

Calculating quadratic expressions using 2x2 matrices

We will calculate quadratic expressions using the 2x2 square matrix x.

Multiply a 2×2 square matrix by a rotation matrix.

We will perform the calculation of multiplying a 2x2 square matrix by a rotation matrix.

Calculating Cubic Expressions for 2x2 Square Matrices

Calculate the cubic expression for a 2x2 square matrix.

Calculate the coefficients and solutions of the characteristic equation of a 2x2 square matrix.

Calculate the eigenvalues of a 2x2 square matrix.

The product of three 3×3 matrices

Calculate the product of three 3x3 square matrices.

Performing calculations related to 3x3 matrices. Part 5

We will perform calculations related to 3x3 square matrices.

Calculate the square root of a 2x2 square matrix.

Calculate the square root of a 2x2 square matrix.

We will perform calculations related to 3x3 square matrices. Part 4.

We will perform calculations related to 3x3 square matrices.

We will perform calculations related to 4x4 matrices.

We will perform calculations related to 4x4 matrices.

Vector Normalization (2-Dimensional)

Normalize (scalar multiply by the identity matrix) a two-dimensional vector to a unit vector.

Calculate the product of three 4×4 matrices.

Calculate the product of three 4×4 matrices.

Calculate the determinant of a 2×2 matrix. (The elements are complex fractions.)

We will calculate the determinant of a 2-row, 2-column matrix.

Vector Normalization (3-Dimensional)

Normalizes a 3D vector.

Vector Normalization (4-Dimensional)

Normalize a four-dimensional vector.

Calculate the coefficients of the characteristic equation (cubic). (Fractions, complex numbers)

Calculate the coefficients of the third-order characteristic equation.

Compute the scalar triple product.

We will calculate a scalar triple product.

Diagonalization of a 3×3 symmetric matrix

We will perform numerical diagonalization on real symmetric matrices.

The value of cosθ in the dot product of vectors.

Calculate the value of the cosine cosθ of the dot product of vectors a and b.

The value of the cosine cosθ of a vector's dot product (3-dimensional vector)

Calculate the value of the cosine cosθ of the dot product of two vectors a and b.

Coefficients of a fourth-degree polynomial

We will derive the coefficients of a quartic polynomial.

Calculating the direction cosine of a vector

Calculate the direction cosine of a 3D vector.

The orthogonal projection of a vector onto a line passing through the origin

We will calculate the orthogonal projection of a vector.

Derivation of the Coefficients of the Characteristic Equation (5th Order)

We will derive the coefficients of the characteristic equation.

Calculate the nth power of a quaternion.

Calculate the nth power of a quaternion.

We will perform quaternion calculations.

We will perform quaternion calculations.

Levi-Civita's symbol (3 letters)

Displays the values of the Levi-Civita symbols.

Levi-Civita notation (4 characters)

Displays the values of the Levi-Civita symbols.

Levi-Civita notation (5 characters)

Displays the values of the Levi-Civita symbols.

Sign and Indices of a Determinant (3rd Order)

Outputs the signs and subscripts used in the determinant expansion.

Sign and Indices of a Determinant (4th Order)

Outputs the signs and subscripts used in the determinant expansion.

Sign and Indices of a Determinant (5th Order)

Outputs the signs and subscripts used in the determinant expansion.

Calculating Linear Expressions Using Quaternions

Calculate the value of a linear expression using quaternions.

Calculating Quadratic Expressions Using Quaternions

Calculate the value of a quadratic expression using quaternions.

Calculating Cubic Polynomials Using Quaternions

Calculate the value of a cubic polynomial using quaternions.

Calculate the product of two octonions.

Calculate the product of eight-vectors.

Output of Gamma Function Tables

Outputs a table of gamma function values.

Calculations involving quadratic functions.

Let's calculate quadratic functions.

Official Cardano-related content.

We will perform some calculations related to the Cardano formula.

"Relationship Between Roots and Coefficients" of Quadratic Equations (Starting from the Roots)

We will calculate the "relationship between the roots and coefficients" of a quadratic equation.

"The Relationship Between Roots and Coefficients" in Quadratic Equations (Based on Coefficients)

We will calculate the "relationship between the roots and coefficients" of a quadratic equation.

"Relationship Between Roots and Coefficients" of a Cubic Equation (Based on Coefficients)

We will calculate the "relationship between the roots and coefficients" of a cubic equation.

"Relationship Between Roots and Coefficients" of a Cubic Equation (From the Roots)

We will calculate the "relationship between the roots and coefficients" of a cubic equation.

The y-intercept and x-intercept of a linear function (from the given equation)

Given the equation of a linear function, find its y-intercept and x-intercept.

Phase angle of a complex number (in degrees)

We will determine the magnitude of the argument θ of the complex number z in degrees.

Changes in the Argument of Complex Numbers Due to Arithmetic Operations (in Degrees)

Using two complex numbers, a and b, we will examine how the argument changes as a result of the four basic operations on complex numbers.

Change in Phase Angle Due to Multiplication of Complex Numbers (Degree Notation)

We will examine how the phase angle changes as a result of multiplying complex numbers.

Let's do some division.

Let's do some division.

Roll a 10-sided die. (3 red, 3 blue, and 3 black)

We will conduct an experiment in which we roll a 10-sided die.

Generating Complex Random Numbers

Generates random complex numbers.

Generating Complex Random Numbers (2)

Generates random complex numbers.

Roll a six-sided, lopsided die

Roll a six-sided, distorted die.

Roll a die with 2 to 100 sides. (Set the tolerance)

Roll a die with 2 to 100 sides.

Trials with an n-sided die (integers)

Roll a n-sided die 12 times.

Trial involving three dice A, B, and C (with 1, m, and n sides)

We will conduct an experiment in which we roll three dice.

Trial involving two dice A and B (with m and n sides)

We will conduct an experiment in which we roll two dice.

Trial involving four dice A, B, C, and D (with n1, n2, n3, and n4 faces)

We will conduct an experiment in which we roll four dice.

Rolling a six-sided die (with customizable results)

We will conduct a trial using a six-sided die.

Number of cases. The sum and product of the numbers on two dice.

Let's examine the number of possibilities.

Number of possibilities. Two dice. Sum of the dice

Let's examine the number of possibilities.

Number of possibilities. Two dice. Difference in the numbers rolled

We will conduct an experiment in which we roll two distinguishable dice.

Number of cases. Three dice. Sum and product of the numbers on the dice

Let's calculate the number of possibilities.

We will examine the saying, "One cannon that hits every time is better than a hundred cannons that hit only once in a hundred shots."

Let's calculate a artillery battle between one gun that hits every time and 100 guns that each hit once out of every 100 shots.

An experiment involving drawing one ball from a bag (white ball or red ball)　

We will conduct an experiment in which we place white and red balls in a bag, take one out, record its color, and put it back in the bag.

Shuffle the 13 playing cards.

Shuffle the 13 playing cards.

Calculations Using the Polynomial Theorem (Trinomial)

Let's work through the calculations for the binomial theorem.

We will calculate the coefficients using the binomial theorem (binomial) and list them.

Here, we will discuss the expansion of (A+B+C)^n.

We will calculate the coefficients using the binomial theorem and list them

We will cover the binomial theorem.

An experiment involving drawing lots from two boxes

We will calculate conditional probabilities.

Output of the nCr List

Outputs a list of nCr values.

Output of a Table Listing nCr and nPr

Outputs a list of nCr, nPr, and r!.

The point of intersection between a circle and a line

Calculate the point where a circle and a line intersect.

Number of common points of two parabolas (perpendicular to the axis)

Calculate the number of points where two parabolas intersect.

Points of intersection between a parabola and a line

Calculate the point of intersection between a parabola and a line.

Calculate the length of the line segment along the parabola.

Calculate the length of the line segment along the parabola.

The equation of the tangent line to a parabola passing through a given point

Find the equation of the tangent line drawn from a given point on a parabola.

Determining a Parabola Based on the Position of the Vertex and a Single Point of Passing

A parabola is determined by the position of its vertex and another point through which the curve passes.

Determining a Parabola Based on the Position of the Axis and Two Points It Passes Through

We will determine the parabola.

The length of a line segment along a cubic curve

Calculate the length of a line segment that follows a cubic curve.

Determine a parabola from three points (perpendicular to the axis)

Determine the parabola from three points.

Equation of a tangent line to an ellipse (from the slope)

Let's calculate the tangent to an ellipse.

The intersection of two lines (Hesse's standard form)

Find the x and y coordinates of the point of intersection of two lines expressed in Hesse's standard form.

Equation of a tangent to an ellipse (given the x-coordinate of the point of tangency)

Calculate the equation of the tangent line to an ellipse.

The intersection of an ellipse and a line

Calculate the point of intersection between an ellipse and a line.

Area, major axis, and minor axis of an ellipse in polar coordinates

When an ellipse is expressed in polar coordinates, we perform the relevant calculations.

Calculations Involving the Rotation of a Parabola

We will calculate the equation of a parabola with a slanted axis.

Examples of Maximum and Minimum Problems (Circles and Horizontal Parabolas)

Given the equation x^2 + y^2 = a, find the maximum and minimum values of k in the equation x + y^2 = k.

Calculate the midpoint formula

Let the coordinates of point A be (x1, y1).

Calculate the radius of a sphere (from its volume).

Calculate the radius from the volume of a sphere.

The Law of Universal Gravitation

Let's calculate the law of universal gravitation.

Calculation of Equivalent Spring Constants (Up to 10)

We will calculate the equivalent spring constant.

When the x- and x'-axes coincide (the origin has been shifted)

Assume that the S and S' systems are translational with respect to the x and x' axes.

At normal speed (using lambda)

Assume that the x, y, z, and ct axes of the S0 system are parallel to the x', y', z', and ct' axes of the S1 system.

Calculation of Equivalent Mass

We will calculate the equivalent mass.

Movement that takes resistance into account

Calculate the motion taking drag into account.

Formula (1) for Uniformly Accelerated Motion

We will calculate uniform accelerated motion.

Formula (2) for uniformly accelerated motion. Coordinate calculations

Let's calculate the formula for uniformly accelerated motion.

Coulomb's Law

Let's calculate Coulomb's law (in a vacuum).

Amount of Salt and Amount of Water

Suppose there is M [g] of a saltwater solution with a concentration of n%.

Typhoon Normal Values (Graph)

This graph shows the normal values for typhoons.

Typhoon Normal Values and Ratio Calculations (Graph)

This graph shows the ratio of typhoon activity to the long-term average.

We calculate the price elasticity of demand using arc elasticity (midpoint method).

Calculate the price elasticity of demand.

Calculate the deadweight loss when applying an ad valorem tax.

Calculates deadweight losses and other effects following the imposition of ad valorem taxes.

Calculate the consumption level that maximizes utility.

We will calculate the optimal consumption.

We calculate the increase in the money supply based on the increase in high-powered money.

The increase in the money supply is calculated based on the increase in high-powered money.

We will calculate the government spending multiplier and the tax multiplier.

We will calculate the government spending multiplier and the tax multiplier based on the marginal propensity to consume.

Calculate the surplus analysis for ad valorem taxes.

　Calculate the surplus analysis for an ad valorem tax.

Calculate the derived deposit amount based on the original deposit amount and the reserve ratio.

We calculate the derived deposit balance created through credit creation based on the original deposit balance and the reserve ratio.

Calculate the optimal consumption for a utility function of type min.

We will calculate the optimal consumption level that maximizes utility.

Calculate the surplus analysis for a volume-based tax.

We will calculate the surplus analysis for a volume-based tax.

Calculate the surplus analysis of free trade and tariffs.

We will calculate the surplus analysis for free trade and tariffs.

Calculate the surplus analysis for quantity restrictions.

We will calculate the surplus analysis regarding transaction volume regulations in a perfectly competitive market.

Calculate the surplus analysis for price regulation.

Calculate the surplus analysis when price regulations are imposed on a perfectly competitive market.

Rewrite the demand function and the inverse demand function in terms of each other.

Rewrite the demand function and the inverse demand function in terms of each other.

Calculate the welfare loss (deadweight loss) in a monopoly market.

Unlike perfectly competitive markets, monopolistic markets result in a loss of welfare (deadweight loss).

Calculate the optimal capital investment amount, K.

Calculate the ratio of capital to output.

Calculate the optimal labor supply

We will calculate the optimal labor supply.

We will calculate the multiplier. (Macroeconomics: Multiplier Theory)

We will cover the multiplier theory in macroeconomics.

We will calculate the theoretical price of the Consol bond.

Here, we will calculate the theoretical price of a Consol bond.

Calculate the money multiplier (credit multiplier) m.

Calculate the money multiplier (credit multiplier) m.

Economic Calculations (Money Multiplier)

Calculate the money multiplier (credit multiplier) m.

Economics Question [Eliminating the Deflation Gap Through Tax Cuts]

I'll work through the economics problems.

Economics Questions [Macroeconomics]

I'll work through the economics problems.

Economics Questions [Microeconomics]

I'll work through the economics problems.

Economics Question (Microeconomics) [Ad Hoc Taxes and Changes in Surplus]

I'll work through the economics problems.

Economics Questions (Macroeconomics) [Proportional Tax, Deflation Gap]

I'm going to work through the calculations for an economics problem.

Performing macroeconomic calculations [45-degree line analysis]

This course covers macroeconomic calculations.

Economics Question (Microeconomics) [Example of Optimal Consumption]

I'll work through the economics problems.

Economics Question [GDP Deflator]

I'll work through the economics problems.

Calculate the shift in the supply curve caused by an ad valorem tax.

Calculate the shift in the supply curve caused by an ad valorem tax.

Economics Question (Microeconomics) [Changes in Equilibrium Under Ad Valorem Taxes]

I'll work through the economics problems.

Supplementary Calculations for the Plum Blossom I Ching

This is the Plum Blossom I Ching.

Calculate the contribution and contribution rate.

Calculate the contribution and contribution rate.

Rolling six eight-sided dice (divination tool)

We will conduct an experiment in which we roll six eight-sided dice.

Rolling an eight-sided die (I Ching divination)

Roll two eight-sided dice and one six-sided die.

Changes in GDP Share Among Major Countries

Select two countries from among several major nations and display the trends in their GDP ratios using a line graph.

Trends in the Ratio of Net Exports to Total Exports and Imports

To calculate net exports, we divide exports by imports.

Determining the World Trigram and the Responding Trigram

We will examine the World Trigram and the Corresponding Trigram in the Money Hexagram.

Length of Service of Past Cabinets

This graph shows the length of service of each Prime Minister in Japan's successive cabinets.

The difference between gross domestic product (expenditure approach) and final demand

Calculate the difference between gross domestic product (expenditure approach) and final demand.

Trends in High-Level Exchanges Between Japan and Israel

This graph shows the number of visits to Israel by Japanese officials and the number of visits to Japan by Israeli officials.

Trends in High-Level Exchanges and Visits Between Japan and the Islamic Republic of Iran

This graph shows the trends in the number of high-level exchanges and visits between Japan and the Islamic Republic of Iran.

Trends in Trade Between Japan and the Rest of the World (April 2024–April 2025)

Here are the trends in the trade balance for fiscal year 2024.

Calculate the Cournot equilibrium.

Calculate the equilibrium of the Cournot model.

Refer to the chronology.

Refer to the Numerology Timeline.

Trends in the Japanese Population by Prefecture

Let's look at the trends in the Japanese population by prefecture.

Trends in Scramble Operations by the Japan Air Self-Defense Force

This chart shows the trend in the number of scrambles conducted by the Japan Air Self-Defense Force (by fiscal year).

Calculating Equilibrium National Income [Macroeconomics]

We will calculate the equilibrium national income.