The Qur’an, the holy book of Islam, does not explicitly discuss mathematics as a subject. However, it contains verses that have inspired and been interpreted in ways that relate to mathematical concepts and encourage the pursuit of knowledge, including mathematics. Let’s explore the relationship between the Qur’an and mathematics.

The Qur’an places a strong emphasis on the pursuit of knowledge. Verses like

- “Say: ‘Are those who know equal to those who do not know?’ Only they will remember [who are] people of understanding.” (Qur’an 39:9)
- “Read in the name of your Lord who created.” (Qur’an 96:1)

These verses have been interpreted as encouraging the study of all fields of knowledge, including mathematics.

## Determination of Qiblah

The determination of the Qibla, the direction Muslims face during prayer towards the Kaaba in Mecca, indeed requires precise mathematical and geometrical calculations. This has been a significant aspect of Islamic scholarship, combining religious obligations with advanced scientific and mathematical knowledge. Here’s a detailed explanation of how accurate mathematical and geometrical measurements are involved in finding the Qibla:

### Historical Context

**Early Methods:**

Initially, Muslims used basic geographical knowledge and natural landmarks to determine the Qibla. As the Muslim world expanded, more accurate methods were needed.**Development of Astronomy and Geography:**

Islamic scholars advanced in the fields of astronomy and geography to ensure accurate determination of the Qibla. This led to the development of sophisticated mathematical methods and instruments.

### Mathematical and Geometrical Principles

**Spherical Geometry:**

**Great Circle Route:**

The most accurate way to determine the direction to Mecca from any location on Earth is to calculate the great circle route (the shortest path between two points on a sphere). This requires understanding the spherical geometry.**Spherical Trigonometry:**

Spherical trigonometry is used to solve problems related to the angles and distances on a sphere. Key equations and laws, such as the law of cosines for spherical triangles, are applied.

**Longitude and Latitude:**

- To determine the Qibla, the latitude and longitude of both the location of the person and Mecca must be known. These geographical coordinates are used to calculate the initial bearing, which is the angle relative to the north direction.

**Mathematical Formulas:**

**Haversine Formula:**

The haversine formula calculates the distance between two points on a sphere using their longitudes and latitudes. This is important for determining the Qibla direction.**Azimuth Calculation:**

The azimuth angle, which is the compass direction from a specific point to another point, can be calculated using trigonometric functions based on latitude and longitude coordinates.

### Instruments and Tools

**Astrolabe:**

- An ancient instrument used by Islamic astronomers to solve problems related to time and the position of the stars. It was instrumental in finding the Qibla direction.

**Qibla Finder Apps and Software:**

- In modern times, digital tools and apps use the same principles of spherical geometry and geographical coordinates to provide accurate Qibla directions.

The determination of the Qibla direction exemplifies the fusion of religious practice and scientific inquiry in Islamic tradition. Accurate mathematical and geometrical measurements are fundamental to ensuring that Muslims worldwide can face the correct direction during prayer. This requirement has historically driven advancements in various scientific fields, vis. mathematics, geography, and astronomy, reflecting the deep connection between faith and reason in Islamic culture.

## Inheritance Calculations in Shariah Law

Shariah law, as outlined in the Qur’an, provides detailed instructions for the distribution of inheritance, which necessitates a precise understanding of mathematics. For a Mufti (an Islamic legal scholar) to calculate these shares correctly, they must be proficient in mathematical concepts and operations. Here are some examples of how mathematical calculations are required in this context:

**Fractional Distribution:**The Qur’an specifies exact fractions for different heirs. For instance:- “Allah instructs you concerning your children: for the male, what is equal to the share of two females. But if there are (only) daughters, two or more, it is two-thirds of one’s estate for them. And if there is only one, for her is half.” (Qur’an 4:11)
- These calculations often involve determining the least common multiple to distribute the estate without remainder and ensuring all shares add to the whole.

## Mathematical Patterns and Structure:

Some scholars and researchers point to numerical patterns and structures within the Qur’an itself that they argue indicate a deeper mathematical order—for instance, the use of certain numbers and their repetitions within the text.

### Significance of Number 19

The first Ayah of the Qur’an is بسم اللّٰہ الرحمٰن الرحیم (Bismillah ar-Rahman al-Rahim) and contains 19 Arabic letters in total. The main theme of the Qur’an is the Oneness of God Almighty (Tawheed).

Miraculously, each word from the first Ayah of the Qur’an appears in the entire Qur’anic text either 19 times or in multiples of 19:

a. **اسْمِ (Ism)** is repeated 19 times in the Qur’an.

b. **اللَّهِ (Allah)** is repeated 2,698 times in the Qur’an, which is 19 x 142.

c. **رَّحْمَنِ (Rahman)** is repeated 57 times in the Qur’an, which is 19 x 3.

d. **رَّحِيم (Rahim)** is repeated 114 times in the Qur’an, which is 19 x 6.

In Arabic, the word for one is Wahid واحد. When we calculate the Abjad numerical values (Gematrical Values) of واحد it makes a total of 19 (6+1+8+4=19). This means that number 19 is related to *Tawheed* (Oneness of God). Surprisingly, the word number one واحد appears only in 19 verses, where it refers to God Almighty. The word Allah (the name of God in Arabic) appears 2,698 times, which is divisible by 19.

Amazingly, the Arabic word for 19 is تسعۃ عشرۃ Tis’ah Asharah, whose Abjad numerical value is exactly 1900, again a multiple of 19. The word تسعۃ عشرۃ appears in the Qur’an only once, in Surah Al-Muddathir (Chapter 74:30), emphasizing the Oneness of God.

### Earth, Sun, Moon

**Earth’s Rotation and Solar Year:**

**One Solar Year:**When Earth completes one full orbit around the Sun, this is considered one solar year.**Earth’s Rotation:**During this period, Earth rotates around its axis approximately 365 times. Hence, there are about 365.25 days in a solar year. The square root of 365.25 is 19.112 which is very close to 19.

**Moon’s Rotation and Lunar Month:**

**Lunar Cycle:**Within one solar year, the Moon completes about 12 full orbits around the Earth. Each orbit or lunar cycle takes roughly 29.5 days, making up what we call a lunar month. A longer Lunar cycle continues for 19 years. After every 19 years, the dates of the lunar months fall exactly on the same days.

### Qur’anic Terminology and Mathematical Correspondences

**Qur’anic Word Counts:**

**Days (يوم and يوما):**According to “*Indexed Dictionary of Qur’anic Terms*” by Muhammad Fuad Abdul-Baqi, the words for ‘day’ and ‘a day’ (يوم and يوما) in the singular form are repeated 365 times in the Qur’an. This corresponds to the number of days in a solar year.**Months (شهر and شهرا):**The words for ‘month’ and ‘a month’ (شهر and شهرا) in the singular form appear 12 times, corresponding to the number of lunar months in a solar year.

**Counting Specific Words:**

- The words are counted in their singular forms because in Arabic, a year is expressed as 365 يوم (singular) rather than أيام (plural), and similarly, a year is 12 شهر (singular) rather than شهور (plural).

### Astronomical and Qur’anic Synchronization

**Script-Based Counting:**

- Some words like يومئذ (that day), يومهم (their day), and يومكم (your day) are not counted in the singular form because they are attached to other words. In contrast, if they had been written separately (like يوم إذ), they might have been included.

**Total Word Occurrences:**

- When all related forms of ‘day’ (يوم, يوما, يومئذ, يومهم, يومكم, أيام, and يومين) are counted together, they total 475 occurrences in the Qur’an. This figure has a unique astronomical significance.
- The singular and plural forms for star/s (النجم، النجوم، الکوکب، الکواکب) appear in the Qur’an 19 times.
- Only 19 verses in which the apparently largest celestial bodies, the sun, and moon, (الشمس، القمر) are mentioned together in pairs.

The idea that the Sun and the Moon start transversing the ecliptic or zodiac after approximately 19 years from a specific point, such as Al-Sharatan (a star in the constellation Aries, also known as Beta Arietis), is related to the concept of the Metonic cycle. Let’s break this down for clarity:

### Metonic Cycle

**Definition:**

- The Metonic cycle is a period of approximately 19 years after which the phases of the Moon repeat on the same days of the year, or almost precisely so.

**Synchronization of Solar and Lunar Calendars:**

- This cycle is significant because 19 solar years are almost exactly equal to 235 lunar months. This means that the positions of the Sun and the Moon will be very similar after 19 years.

### Relation to Al-Sharatan and the Zodiac

*Al-Sharatan*is one of the stars in the constellation Aries. In historical and astronomical contexts,*Al-Sharatan*is often considered the starting point of the zodiac.

- The ecliptic is the apparent path of the Sun across the sky, which is also followed closely by the Moon and the planets. The zodiac is a belt of the sky extending about 8 degrees north or south of the ecliptic, divided into twelve signs.

### Sun, Moon, and the Ecliptic

**Ecliptic Cycle and Metonic Cycle:**

- While the Sun follows the ecliptic over the course of a year, the Moon’s path intersects the ecliptic at points called the lunar nodes. These nodes regress around the ecliptic over a period of about 18.6 years, which is close to the 19-year Metonic cycle.

**Ecliptic Longitude Reset:**

- After approximately 19 years, the positions of the Sun and the Moon relative to the ecliptic and the zodiac signs will have completed a cycle, meaning they will appear in nearly the same positions in the sky as they did 19 years earlier.

**475 Earth Days in Sun’s 19 Rotations:**- The day of any celestial body, like a star or planet, is defined by its rotation period.
- The Sun completes 19 rotations around its axis in about 475 Earth days (19 x 25 = 475).

This intricate alignment suggests a profound connection between the textual structure of the Qur’an and astronomical phenomena, reflecting the sophisticated interplay between language and the cosmos in Islamic tradition. This miraculous synchronization of the astronomical data with the Quranic language is so surprising and compelling to believe in the Divine origin of the Qur’an. Only, the all-Knowing and Omnipotent God Almighty could compose such a Scripture like the Qur’an.

In summary, while the Qur’an does not teach mathematics directly, it encourages the pursuit of knowledge, including mathematical understanding, and contains elements that relate to mathematical principles.