Author: tonagai

Formula for calculating stroke risk

This calculates the probability of having a stroke over a 10-year period (according to the National Cancer Center).

Apgar Score (Newborn Health Assessment)

This tool calculates the APGAR score (APGAR test, APGAR index), a system developed by Virginia Apgar to assess the health of newborns.

The SIR Model (Differential Equations for COVID-19 Transmission)

We will calculate the SIR model, the simplest model for describing the spread of infectious diseases.

The SEIR Model (Differential Equations of COVID-19 Infection, Part 2)

Following the SIR model, we will calculate the SEIR model, which represents the spread of infectious diseases.

The time left to spend with my parents (rather than getting scolded by Chiko-chan)

This is the equation derived by Professor Yasuda of the Department of Sociology at Kansai University, as featured on the NHK program *Chico-chan ni Shikarareru*.

Formula for predicting daily water balance (metabolic turnover) in the human body

We will calculate the formula published in the scientific journal *Science* by Yosuke Yamada, Director of the National Institute of Biomedical Innovation, Health and Nutrition, and his colleagues in collaboration with researchers from the United States, the United Kingdom, the Netherlands, and other countries, which estimates how much water the human body loses each day.

How old would your dog or cat be in human years?

This tool calculates your dog or cat’s age in human years.

Surplus calculations (pharmacies and distribution warehouses)

Since the Casio MP-12R calculator, which can calculate remainders, is so popular, I decided to build my own version that can do the same thing.

The Formula for the Perfect Hard-Boiled Egg (by Peter Barham)

Here is the formula for making the perfect hard-boiled egg.

When it rains, which gets you wetter—running or walking? (The "Run in the Rain" Rule)

We will calculate the “Runnin’ in the Rain Formula” (RiR), which appeared in an article by Hiroo Ito titled “The Runnin’ in the Rain Formula: The Difference in How Wet You Get When Running vs. Walking in the Rain” in the June 2020 issue of *Math Seminar*.

Linear regression estimation of required heating times and quantities for frozen foods, milk, and other items where such information is not provided

Packages for frozen foods like fried chicken and baby formula list the number of servings, microwave heating times, and weight-to-formula ratios, but sometimes they don’t include the specific number of servings or weight you’re looking for.

Calculating Your Destiny Number (from the "Yarisu Cozy" urban legend)

Your destiny number is the sum of the digits of your date of birth.

Senso-ji Temple Fortune Slip Simulator

It is said that the fortune slips at Senso-ji Temple often predict bad luck.

The Kiyoshi Function (Zun, Zun, Zun, Zundoko)

Generates 5 "Zun" and "Doko" sounds at random.

Stride, Pace, and Time (2021 National Center Test for University Admissions—Mathematics)

Question 2 of the 2021 Common Test in Mathematics IA was about pitch and stride.

Your life is tens of thousands of kilometers of film (more than 1.15 million kilometers of film—

The title of Official Hige Dandism's song "1.15 Million Kilometers of Film" comes from the fact that 35mm film runs at 24 frames per second and uses 1.5 feet (1 foot = 0.3048 m) of film per second.

Show Calculation (Sayaka's Routine)

Here is the "Sayaka" routine from the 2023 M-1 Grand Prix Finals—it's a math demonstration.

The probability of getting nothing but misses no matter how many times you try the gacha

Don't you think that if you pull a gacha with a 1% drop rate 100 times, you'll get a rare item at least once? That's not how it works at all.

Number Guessing Game

It's a number-guessing game.

How the Birthday Guessing Game Works

Please calculate the number obtained by multiplying the month of your birth by 4, adding 9 to that result, multiplying the whole thing by 25, and then adding your birth date to that number.

Guess My Age Game

I'll guess your age.

A "NKODICE" (Nko Dice) Clone

This is a clone of the popular Steam game "NKODICE (Nko Dice)."

Numberle: A Wordle-style game where you guess five numbers

I'm hooked on Wordle, where you have to guess a five-letter English word, so I made a game that does the same thing but with numbers.

"Shika no Ko no Ko no Ko no Ko Shita Tan Tan" Game

The opening theme song “Shika-iro Days” from the TV anime “Shikano Konoko Konoko Kokoshitan Tan” is all the rage right now, so I turned it into a game that uses random numbers, similar to Kiyoshi Game (Zun, Zun, Zun, Zundoko) and NKODICE (Nko Dice).

amicable numbers

Two natural numbers are called amicable numbers if the sum of their proper divisors is equal (this concept also appeared in *The Equation the Doctor Loved*).

Ramanujan's identity for the number of taxis

(x^2 + 9xxy - y^2)^3 + (12x^2 - 4xxy + 2y^2)^3 = (9x^2 - 7xxy - y^2)^3 + (10x^2 + 2y^2)^3 This identity, discovered by Ramanujan, allows us to reproduce the moment when, while hospitalized, Ramanujan heard the taxi number 1729 and immediately replied, "1729 = 1³ + 12³ = 9³ + 10³."

Calculating continued fractions

Calculate the continued fraction (up to the nth term)

Base-n conversion (for any integer n ≤ 34)

Converts a decimal number to a base-n number (where n is any integer ≤ 34).

The Problem of the Beautiful Woman by the Sea (The Problem of Finding a Spouse)

n beautiful women are standing in a row on the beach.

Capreka number (Caprekarutin)

Think of any number you like (we recommend a 3- or 4-digit number).

Fibonacci sequence, Pell sequence, Padovan sequence, Perrin sequence

We will calculate the Fibonacci sequence, the Pell sequence, the Padovan sequence, and the Perrin sequence, and determine the ratios of their adjacent terms.

The Joyce sequence (named after James Joyce's *Ulysses*)

We will calculate the sequence a_n = (n^(n^n) / number of digits), which is inspired by James Joyce's *Ulysses*.

Math Magic (What remains when you add six numbers one after another?)

Write down any six numbers you like.

What happens if you repeatedly square and add each digit of a positive integer?

Think of any positive integer you like; if you add up the squares of its digits, the sum will either equal 1 or fall into the cycle of 4, 16, 37, 58, 89, 145, 42, and 20.

Prosthaphaeresis: Calculating a Product from a Sum, and Logarithmic Tables

As a method for quickly calculating products, it is said that before the 16th century, a technique called "Prosthaphaeresis"—which involves expressing the product as a sum using the formula cos(a)cos(b) = (cos(a+b) + cos(a-b))/2—was used.

Calculating the check digit for an 11-digit number

Calculate the check digit from the 11-digit number.

Divisor function σx(n)

We will compute the divisor function σx(n), which returns the sum of the xth powers of the divisors d of a natural number n.

Calculations Involving Square Residues and the Square Residue Symbol

If the integers a and p are coprime, and the congruence x² ≡ a (mod p) has a solution, then a is called a quadratic residue modulo p.

General Equation of the Ellipse

Ayaka Riri (a science news commentary account) tweeted about Valeriy G. Narushin et al.'s paper "Egg and Math: Introducing a Universal Formula for Egg Shape" (Ann. N. Y. Acad. Sci., 2021), so I decided to try it out on Casio's high-precision calculation website as well.

A Visualization of the Collatz Conjecture

Take any positive integer n. If n is even, divide n by 2. If n is odd, multiply n by 3 and add 1. We will illustrate the Collatz conjecture, which states that repeating this process eventually results in 1.

Number of Chicken McNuggets (Frobanius' Coin Exchange Problem)

In the past, McDonald's in the UK offered Chicken McNuggets in sets of 6, 9, or 20 pieces.

Indeterminate equation a*x + b*y = gcd(a, b) (Bezout's Identity)

Question 4 on the 2022 Common Test for Mathematics I and Mathematics A involved Diophantine equations. The problem required students to find the solutions to the following Diophantine equations: 5^4*x - 2^4*y = 1, 5^5*x - 2^5*y = 1, and 11^5*x - 2^5*y = 1.

The Accuracy of Seki Kōwa and Tatebe Kenkō’s Method for Calculating Arc Lengths from Arrow Heights and Chord Lengths in Japanese Mathematics

In the January 2025 issue of *Nikkei Science*, in the special feature “Rediscovering Wasan,” we’ll examine the accuracy of the approximation formula for the square of an arc—which appears in the article “The True Portrait of Seki Kōwa, the Sage of Mathematics,” by Kenichi Sato—by comparing it with the exact value.

Calculating Pi (Gauss–Legendre’s Arithmetic-Geometric Mean Method)

We will examine the AGM method (Gauss-Legendre algorithm, arithmetic-geometric mean method), the algorithm used by Mr. Takahashi and his colleagues at the University of Tsukuba to calculate pi to 2,576,980,370,000 digits.

Calculating Pi (Ramanujan and Chudnovsky)

We will compare Ramanujan's formula and the Chudnovsky brothers' formula, both of which are known as formulas for calculating pi.

Minimal Solutions to the Perel equation

Find the smallest integer solutions (X, Y) to Pell's equation, X² - NY² = ±1, and the next largest solution.

Poisson random numbers

Generates random numbers following the Poisson distribution: P(X=n) = exp(-λ)λ^n / n!

Twin primes

Two prime numbers whose difference is 2 are called twin primes.

Searching for Lychrel numbers

If you flip 56 to make 65 and add them together, you get 121, which is a palindromic number.

Solving Quintic Equations (Complex Numbers)

We will solve a fifth-degree equation using the DKA method.

Solving Sixth-Degree Equations (Complex Numbers)

We will solve a sixth-degree equation using the DKA method.

Solutions to nth-degree equations (complex numbers, where n is up to 20)

We will solve the nth-degree equation, a(n)*x^n + a(n-1)*x^(n-1) + ... + a1*x + a0 = 0, using the DKA method.

The Pellin sequence (numbers that remain the same when squared; numbers that go on to infinity)

This is a calculation of the Pell's sequence (numbers that return to their original value when squared) as described in *Numbers Reaching to the Sky* (by Fumimoto Kato and Yasuyuki Nakai).

Number of Divisions (From the movie "The Formula Given by a Miracle")

The number of partitions p(n) is the number of ways a natural number n can be expressed as the sum of natural numbers (including n itself), in any order.

Jesus Guillera's formula for calculating pi (π)

Jesús Guillera has discovered a formula for the mathematical constant π that converges incredibly quickly.

Solve a four-variable ordinary differential equation using the Runge-Kutta method (four-stage, fourth-order)

dx/dt = f1(x, y, z, w, t) dy/dt = f2(x, y, z, w, t) \frac{dz}{dt} = f3(x, y, z, w, t) \frac{dw}{dt} = f4(x, y, z, w, t) We will solve these four-variable ordinary differential equations using the Runge-Kutta method (four-stage, fourth-order).

The Newton-Raphson method for two variables

Using the two-variable Newton-Raphson method, we calculate the values of x and y that satisfy f(x, y) = 0 and g(x, y) = 0.

Euler's phi function (tangent function)

For a positive integer n, the number of natural numbers from 1 to n that are coprime to n is denoted by φ(n) and is called Euler's φ-function or the Torsion function.

Lambert's W-function (kth solution)

The Lambert W-function is the inverse function of z = w * exp(w), i.e., w = W(z).

Calculation of Fourier series

Calculate the Fourier series.

Ackermann function Ack(m,n)

Calculate the Ackermann function Ack(m,n).

Determining the Number of Common Elements (Tannell's Theorem)

The sum of the areas is the area of a right triangle in which all side lengths are rational numbers; we will prove this.

Lagrange interpolation (up to 11 points)

We will use Lagrange interpolation to find an nth-degree polynomial that passes through n+1 points, all of which have distinct x-coordinates.

Liouville's Theorem: The Sum of the Squares of the Divisors of a Sum Equals the Sum of the Cubes of the Divisors of That Sum

Let's review the following information from Fermat's Library.

Values of any number of digits of pi (by Simon Plouffe)

In his paper titled “A formula for the nth decimal digit or binary of π and powers of π,” Simon Plouffe presents a formula for calculating the value of pi (π) to any number of decimal places.

A New Formula for Pi Derived from String Theory

Arnab Priya Saha and Aninda Sinha, researchers in string theory from India, derived a new formula for pi in their paper titled “Field Theory Expansions of String Theory Amplitudes.”

2014 National Center Test for University Admissions: Mathematics II and Mathematics B, Question 6

Question 6 on the Heisei 26 National Center Test for University Admissions—Mathematics II and Mathematics B—involved factoring the factorial (N!).

2015 National Center Test for University Admissions: Mathematics 2B (Old Curriculum), Question 6

Let M and N be natural numbers such that M > N and their greatest common divisor is 1.

The Problem with the Mathematical Tablets at Gokō-gū (Fushimi, Kyoto)

This is a problem from the mathematical tablets at Gokō-gū Shrine in Fushimi, Kyoto.

Graphs of the first- and second-order derivatives of the function f(x)

We will calculate the first and second derivatives of the function f(x) and plot them.

Probability of matching birthdays (at least k people out of N)

Calculate the probability that at least k people out of N have the same birthday.

Probability of matching birthdays (2–5 out of N people; displayed as a graph)

I will create a graph showing the probability that two people have the same birthday.

Distribution of the Ratio (Quotient) of a Normal Distribution: Fieller-Hinkley

Calculate the distribution of the ratio (quotient) of two normal distributions, X1 and X2: X1/X2.

Pearson's chi-square test (goodness of fit)

We will perform Pearson's chi-square test (goodness-of-fit test).

Pearson's chi-square test (independence)

We will perform Pearson's chi-squared test (test of independence).

One-sample t-test

We will perform a one-sample t-test.

Hypothesis Test for the Difference Between Two Proportions

We will perform a test to determine whether there is a difference in the proportions between the two groups.

t-test for the difference between the means of two groups

We will perform a t-test to compare the differences between the two groups in the absence of a matched pair.

Determining Sample Size (Testing a Single Population Mean)

When conducting a one-sample t-test, calculate the required sample size given the effect size (Δ = (μ - μ₀)/σ—how many times the standard deviation is the difference in means?) and the significance level.

Determining Sample Size (When Testing the Difference Between Two Means)

When conducting a test for the difference between two means, given the effect size (Δ = (μ1 - μ2) / σ—how many times the standard deviation is the difference between the means?) and the significance level, calculate the required sample size n (where n = n1 = n2, indicating the sample sizes for each group).

Power Curve (for the difference between two means)

Calculate the power curve (1-β for the case where the difference between two means is μ1 - μ2).

Power curve (for a single mean)

Calculate the power curve (1-β for a single mean).

Testing the Correlation Coefficient

We will perform a test of the correlation coefficient.

Simple Linear Regression (t-Test and Confidence Intervals)

Calculate the t-test and confidence intervals for the regression coefficients a and b (slope and intercept) in simple linear regression (y = ax + b).

Estimation of the confidence interval for the population proportion

We estimate the confidence interval for the population proportion—such as determining whether a candidate is certain to win based on the vote share from exit polls—to determine whether a candidate is certain to win.

Probability of correctness (the probability that a group, deciding by majority vote, is correct)

We will calculate the probability of validity—also known as Condorcet’s jury theorem—which also appears in Yuto Ichikawa’s novel *The Closed Room of God and the Ripples*.

A function that draws a heart

y = (sqrt(cos(x)) * cos(400*x) + sqrt(abs(x)) - 0.4) * (4 - x*x)^0.1 is a function that draws a heart (as seen in Google's graphing tool).

Calculate the height that halves the volume of a frustum

This is a formula for calculating the height at which a frustum of a cone can be divided into two equal parts—similar to a problem like, “At what point should you cut a carrot to reduce its volume by half?”

The Five Centers of a Triangle (Center of Gravity, Incenter, Circumcenter, Orthocenter, Excenter)

Enter the coordinates of the vertices of triangle ABC, and the program will calculate the coordinates of the five centers of the triangle (centroid, incenter, circumcenter, orthocenter, and excenter).

Coordinates of the vertices of a regular polygon

Calculate the vertices of a regular polygon.

Finding the arc length, chord length, and height of an ellipse using the semi-major axis, semi-minor axis, and central angle

Enter the major axis radius, minor axis radius, and central angle of the ellipse to calculate the arc length L, chord length d, and height h.

Given any two of the following: arc length, chord length, height, or radius, calculate the remaining value

Enter values for any two of the following: arc length (L), chord length (d), arc height (h), and radius (r). Then, enter 0 for the remaining two (do not leave them blank), and the program will calculate those two values and the central angle.

Find the other diameter of an ellipse given its circumference and one of its diameters.

Calculate the other radius of an ellipse given its circumference and one of its radii (either the major or minor radius).

Circumference and Area of a Hyperellipse (Lame Curve)

Hyperellipse (Lame curve) |x/a|^n + |y/b|^n = 1 (a standard ellipse when n=2) We will calculate the circumference and area of this hyperellipse.

Energy levels of the hydrogen atom in relativistic theory (solutions to the Dirac equation)

We will calculate the energy levels of the hydrogen atom (Z = 1) using the Dirac equation, which is a fundamental equation of relativistic quantum mechanics.

Calculation of the diamagnetic coefficient (ellipsoid)

Calculate the magnetic field coefficients Nx, Ny, and Nz for the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1.

Holzmann functions H(β) and G(β) & mean lifetime τ(β)

The Holtzmark distribution describes the distribution of stars when they are randomly distributed in three dimensions, as observed from a single point under the influence of gravity.

The relationship between the drag coefficient (C_D) of a sphere and the Reynolds number (Re)

We will calculate the drag coefficient (CD) of a sphere using the Reynolds number (Re).

Compute the logistic map to 50 decimal places using three different initial values

Using the famous logistic map that illustrates chaos, xn+1 = a*xn*(1-xn), we will see how the values diverge even with just a slight change in the initial value.

Forces Acting on a Submerged Door

When water from a flood or other source reaches the door, even if the water isn't very deep, the door will no longer open.

The Relationship Between Altitude and the Boiling Point of Water

It is well known that the boiling point of water decreases with increasing altitude; here, we will perform an approximate calculation.

Dielectric constant of mixtures (Maxwell-Garnett model)

This calculates the effective permittivity when powders or other substances are mixed into a medium (such as resin).

Frequency-dependent dielectric constants of water and ice (dielectric dispersion)

Calculate the frequency dependence (dielectric dispersion) of the complex permittivity of water and ice.

The Universal Law of Procrastination (Deadlines, Homework, Progress, etc.)

Summer vacation homework, assignments due, application forms, research progress—people tend to put these things off until the very last minute.

Temperature-dependent properties of water’s viscosity, kinematic viscosity, and density

Apparently, the reason the sound of pouring hot water sounds different from the sound of pouring cold water is that the viscosity of water varies significantly with temperature.

Absorption Spectrum of Hemoglobin (Principle of Pulse Oximeters)

This graph illustrates the principle behind pulse oximeters—which gained attention during the COVID-19 pandemic—by showing the wavelength-dependent difference in the molar extinction coefficients between hemoglobin bound to oxygen (HbO₂) and hemoglobin that has released oxygen (Hb) (Please press the "Calculate" button first, then the "Graph" button).

Wavelength of electromagnetic waves, reflectivity, transmittance, half-power depth, skin thickness

Calculates the wavelength, reflectance, transmittance, half-power penetration depth, and epidermal thickness of electromagnetic waves.

How many planets are there that host extraterrestrial life? (The Drake Equation)

We'll calculate the Drake Equation to determine how many planets host extraterrestrial life.

Density Distribution of the Earth's Interior Based on PREM

This figure illustrates the density distribution of the Earth's interior based on the PREM (Preliminary Reference Earth Model).

Gravitational acceleration g inside and outside the Earth, as determined by PREM

This program calculates the gravitational acceleration inside and outside the Earth using the PREM (Preliminary Reference Earth Model).

Convert VSWR to return loss.

Convert the voltage standing wave ratio (VSWR) to return loss.

Characteristic impedance of a stripline

Calculate the characteristic impedance of the stripline.

Convert return loss to VSWR.

Convert reflection loss (return loss) to voltage standing wave ratio (VSWR).

Calculation of the B-coefficient for an NTC thermistor

The B-constant of a thermistor is calculated using the formula B = ln(Rb/Ra) / (1/(273.15 + Tb) - 1/(273.15 + Ta)).

Temperature Characteristics of NTC Thermistors (Calculated Using the B-Constant)

The temperature characteristics of an NTC thermistor are calculated using the following equation: R = R0 * exp (B * (1/T - 1/T0)) .

Characteristic Impedance of a Microstrip Line

Calculate the characteristic impedance of a microstrip line.

Antenna gain of a standard gain horn antenna

Calculate the antenna gain (in dBi) of a waveguide-fed standard gain horn antenna (pyramidal horn).

Graph of Thermistor Temperature Characteristics (Steinhart-Hart)

The temperature coefficient of a thermistor is calculated using the equation 1/T = a + b*ln(R) + c*ln(R)^3.

Calculation of the Steinhart-Hart Parameters for a Thermistor

Based on the Steinhart-Hart equation for thermistor temperature characteristics, 1/T = a + b*ln(R) + c*ln(R)^3, this function calculates the parameters a, b, and c when you input the temperature and resistance values at three points.

Converting impedance to reflection coefficient (two definitions)

The reflection coefficient is calculated from the load impedance and the characteristic impedance.

Parameter Estimation for the Weibull Distribution

This calculates the parameters m and η, as well as the mean lifetime μ, for the Weibull distribution f(t) = (m/η) * (t/η)^m * exp[-(t/η)^m], which is used to analyze the lifetimes of components and other items.

Calculation of the High-Frequency Impedance of a Cylindrical Conductor (Including the Skin Effect)

Calculate the high-frequency impedance of a cylindrical conductor.

Design of Microstrip Patch Antennas (Efficiency and Antenna Gain)

We will design a rectangular microstrip antenna.

Three Models of Electrical Conductivity Based on Surface Roughness of Conductors

The high-frequency electrical conductivity (resistivity) of a conductor varies depending on its surface roughness.

Risk of Electric Shock (Symptoms Based on Body Current and Duration of Exposure)

Even at low voltages, it is dangerous if an electric current flows through the human body.

Calculation of 2-port S-parameters for T-type circuits

Calculate the S-parameters for a T-type circuit.

Calculation of 2-port S-parameters for π-type circuits

Calculate the S-parameters for a π-type circuit.

S-parameters of a microstrip line (including losses)

After calculating the characteristic impedance of the microstrip line using the Hammerstad and Jensen models, we calculated the conductor loss (including roughness according to the Morgan model) and the dielectric loss, and converted these values to S-parameters while taking the imaginary part of the characteristic impedance into account.

S-parameters of a strip line (including losses)

After calculating the characteristic impedance of the stripline, we calculate the conductor loss (including roughness according to the Morgan model) and the dielectric loss, and convert these values to S-parameters while taking the imaginary part of the characteristic impedance into account.

Maximum radar detection range (based on the radar equation)

We calculate the maximum detection range of the radar using the radar equation: Pr = Pt * G² * λ² * σ / [(4π)³ * R⁴].

Input impedance of a load connected to a transmission line

This calculates the input impedance when a transmission line with characteristic impedance Zo, length L, effective permittivity εeff, and loss factor α is connected to a load impedance ZL (input as a function of ω).

Lifetime Prediction of Multilayer Ceramic Capacitors (MLCCs) Using Accelerated Testing

This is an empirical formula used to predict the service life of multilayer ceramic capacitors (MLCCs) in the market.

Equivalent Circuit Calculations for Crystal Oscillators

Calculate the magnitude of the impedance (in log units) and the phase (in degrees) from the equivalent circuit of a quartz crystal oscillator.

Conversion Between T-Type and π-Type Circuits

This tool converts between three types of impedance for T-type and π-type circuits.

Temperature-Humidity Acceleration Model (Hallberg-Peck model)

When conducting accelerated testing under high-temperature and high-humidity conditions, we calculate the Hallberg-Peck model, which is based on relative humidity.

Design of π-Type and T-Type Attenuators (Impedance Matching)

We will design an attenuator capable of impedance matching.

Calculating Sample Size for A/B Testing

Calculate the sample size required for an A/B test.

Verification of RSA Encryption (From NHK’s “Math Without Laughter,” Cryptography)

We'll examine the RSA cipher featured in the NHK program *Cryptography in Math Without Laughter*, which stars Mr. Ogata of the group Panther.

Calculating the Break-Even Point

Calculate the break-even point, break-even ratio, contribution margin, and contribution margin ratio.

The negative binomial distribution model (NBD model), which describes the probability of the number of purchases

We will calculate the negative binomial distribution (NBD) model, which is used in mathematical marketing to represent the probability of the number of purchases.

Calculation of the parameter K in the negative binomial distribution (NBD) model

We will use the Newton-Raphson method to calculate K, the parameter that determines the probability distribution in the negative binomial distribution (NBD) model—which is used in mathematical marketing to represent the probability of the number of purchases.

Delishley NBD Model: Probability of purchasing the company’s own brand within a category

We will calculate the Dirichlet NBD model (commonly known as the Dirichlet model), which is used in mathematical marketing to represent the probability of purchasing a company's own brand within a given category.

Delishley NBD Model: Own-brand purchase rate: Probability of purchase

We use the Dirichlet NBD model (commonly known as the Dirichlet model), which is used in mathematical marketing to represent the probability of purchasing a company’s own brand within a category, to calculate the purchase rate and the number of purchases.

Calculation of Parameter S for the Delishley NBD Model

We calculate the parameter S—which appears in the Dirichlet NBD model (commonly known as the Dirichlet model)—used in mathematical marketing to represent the probability of purchasing a company’s own brand within a category, based on actual purchase rates of the company’s own brand.

Gamma-Poisson-Lehsen Model

We will calculate a Gamma-Poisson recency model that predicts "When was the last purchase?" and "When was the last visit?"

Calculation of m and k in the Gamma-Poisson-Lisenzi Model

We calculate the parameters m and k that appear in the Gamma-Poisson-Licenzy model, which predicts “When was the last purchase?” and “When was the last visit?”, using the quasi-Newton method.

The Shrikuma function (calculating surface area based on the height and foreleg circumference of an Indian elephant)

This is the formula for calculating the surface area of an Indian elephant, which won the Ig Nobel Prize.

The Formula for the Probability of a Merry Christmas

From a Daily Mail article titled “Mathematicians Create a Formula for the Perfect Christmas Day, and Say the Key Is Turning OFF the TV.”

FizzBuzz

Starting with 1 and counting up, when a number is divisible by 3, it's called "Fizz"; when it's divisible by 5, it's called "Buzz"; and when it's divisible by both 3 and 5, it's called "FizzBuzz."

Tokyo Medical University Entrance Exam Score Simulator

Tokyo Medical University is notorious for irregularities such as lowering scores for female applicants, so we will simulate its entrance exam scores.

The formula relating the total weight of a battleship to its construction cost (from the movie *Archimedes' War*)

This is the equation derived by Nao Kai, the genius mathematician played by Masaki Suda in the movie *Archimedes' War*, showing the relationship between the total amount of iron and the cost of building a battleship.

The direction to face when eating Setsubun ehomaki

Enter the year you want to check (the default is this year), and it will display the direction in which you should eat the entire Ehomaki roll on Setsubun.