Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers.

(Shakuntala Devi, writer and mental calculator)

### The Fibonacci sequence and botany

The Fibonacci sequence and flowers share a mesmerizing connection, revealing the elegance of mathematics within the natural world. The sequence, which starts with 0 and 1, with each subsequent number being the sum of the two preceding ones (0, 1, 1, 2, 3, 5, 8, and so on), appears to be a hidden code governing the growth patterns of various flowers. Many flowers, including sunflowers and daisies, exhibit spirals that follow the Fibonacci sequence. The number of petals in these flowers often corresponds to Fibonacci numbers, such as 3, 5, 8, or 13. This harmonious relationship between mathematics and botany evokes a sense of wonder, suggesting that the Fibonacci sequence serves as an unspoken blueprint guiding the artistry of nature's blossoms.

One of my personal favorite flowers to have in my garden is the Mexican sunflower (*Tithonia rotundifolia*). These orange-to-red sunflowers attract a wide variety of bees, butterflies, and hummingbirds to my backyard. Below is a picture of one from the summer of 2023:

As you can see, this flower has 13 petals. In mathematics, 13 is a very special number with several titles, including:

- Prime – a whole number greater than 1 that cannot be exactly divided by any whole number other than itself and 1.
- Fibonacci – a member of the Fibonacci sequence, detailed previously.
- Fibonacci prime – a Fibonacci number that is prime.
- A member of a Pythagorean triple (5, 12, 13). You’ll likely remember these sets of numbers from geometry, where they describe the whole number lengths of right triangles. The Pythagorean Theorem told us that the square of the lengths of the two shorter sides (a and b) equaled the square of the longer side --- aka the hypotenuse, the side across from the right (90 degrees) angle: a
^{2}+ b^{2}= c^{2}.

### The Fibonacci sequence and birds

The connections between the Fibonacci sequence and the flights of birds reveal a remarkable harmony between mathematics and the avian world. Some species of birds exhibit flight patterns that align with the Fibonacci sequence, highlighting nature's propensity for following mathematical principles. When birds take to the skies, their wing motions often follow specific ratios that correspond to consecutive Fibonacci numbers, resulting in graceful and efficient flight paths. Additionally, the arrangement of feathers on a bird's wing may also adhere to the Fibonacci sequence, further emphasizing the prevalence of this mathematical phenomenon in the avian realm. The captivating synchrony between the Fibonacci sequence and the flights of birds underscores the elegance of nature's design, allowing these feathered creatures to soar through the air with both grace and precision.

### The Fibonacci sequence and the stars

The unknown code of reality seems to also write itself on a grand scale. The connection between the Fibonacci sequence and stars lies in the arrangement and distribution of stars within certain celestial objects, particularly in spiral galaxies. Spiral galaxies, such as the famous Andromeda galaxy and our own Milky Way, showcase a pattern that closely resembles the Fibonacci sequence.

In these galaxies, stars are organized in logarithmic spirals that follow a specific pattern. The number of arms or spiral patterns in these galaxies often corresponds to Fibonacci numbers, such as 2, 3, 5, 8, or 13. Additionally, the angles between these spirals, measured in degrees, also exhibit relationships found in the Fibonacci sequence.

The phenomenon is known as "Fibonacci spirals" or "Fibonacci galaxies." These visually striking patterns are a testament to the fundamental principles of mathematics imprinted upon the vast canvas of the cosmos. This connection between the Fibonacci sequence and stars in the sky is yet another awe-inspiring example of the natural world's inherent mathematical elegance and the enigmatic harmony between science and the universe. From sunflowers to birds, to the universe, there are mathematical equations at work, waiting to be solved.

### Application of mathematics to the paranormal

To learn more about paranormal phenomena such as UFOs (UAPs), there is a great need for data. It is important to acknowledge that although public transparency of such data is an integral step in disclosure, it is understandable that there is also a need for classified information in regard to security matters. This makes the public gathering of data even more important, and the more sources, the better. Information from Avi Loeb’s Galileo Project, NASA, MUFON, and private individuals observing the skies (which remain unclassified) should be gathered and analyzed. This is the scientific method. It is through such rigorous science that conclusions can be drawn. I started growing Mexican sunflowers in my home garden several years ago. Not only are they beautiful, but their orange-to-red sunflowers attract a wide variety of bees, butterflies, and hummingbirds to my backyard.

The discovery of connections such as that between mathematics and botany, birds, and stars took data and analysis – hard science. But such relationships would go unknown without those who dedicate themselves to the effort of collecting data and making it available to the public. I suspect there are beautiful mathematical relationships to be discovered within UFOs and other paranormal phenomena, but there is a severe lack of public data. Certainly, the military has collected data, but the mathematics seem to remain locked away, accessible only to a select few. These high-level figures within our government, military, and private contractors are able to maintain a veil of secrecy on data they deem too classified for public consumption. However, thanks to historic events like the July 26th Congressional Oversight UFO Hearing (video below), the days of shadowy access to under-the-table Special Access Programs (SAPs) could be coming to an end.

Something that has been said for quite a while is that if we are to ever communicate with alien beings, the common language would be mathematics. I also believe that gaining a deeper understanding of UFOs and UAPs is possible through mathematics: the gathering and analysis of large amounts of data. Shape, color, size, location, speed, etc. I am convinced that once this begins to widely take place, humankind will discover an unspoken blueprint guiding the artistry of the universe's deepest mysteries.