Thinking about arts and mathematics, people always see two distinct disciplines characterized by different characteristics. The connection between the two seems distantly separated that very few stop to reason the relationships between the two. For many, mathematics is often treated as a cognitive, rational, thinking, and a left-brain kind of activity as demonstrated in EU gains.Ca selection of materials for math classes. On the other hand, art has been viewed as a simple effecting feeling discipline associated with the right brain.

The assumed distinction between arts and mathematics has been the basis for which teaching of the two subjects is undertaken in classes. For many, the science or art of math is an enigma subject or area of specialization characterized by an impression of complex intertwining of numbers and tough calculations. Comparably, many have argued that math subjects are brain boggling compared to the art subjects. For these reasons, many have associated math subjects with a feeling of rejection, disinterestedness. However, the separation between math and art sits very wearily between the two disciplines. For instance, Luis, Idan, and Robert observes that the core of mathematics is often to search for truth and beauty through the use of numbers and formulas to provide concrete truths concerning various phenomena. Many may think that since art subjects are soft subjects, their characteristics sharply contrast those of math subjects.

Despite these many allegations, the connection between art and math is undeniably immense. Math and the Visual Arts are incredibly similar disciplines (Wikipedia.org). The process in math is identical to the creativity in the visual arts, not in the figurative sense that math is a form of art, rather, both use similar parts of the brain and use an identical approach. Consider for instance, how music would be without the mathematical elements such as tempo, time, beats, or measure or how circles and squares would be drawn in artistic compositions without considerable knowledge about mathematical concepts such as geometry and shapes (Escher). Certainly, the relationships between mathematics and art are not as slim as perceptions may guarantee. For instance, the movements in music are often choreographed based on the beats count which is mathematically determined and calculated. Besides, several other art disciplines, including architecture, painting, molding, etc. rely heavily on mathematical concepts to achieve the levels of perfection they require.

According to Ozdural, both art and mathematics can be used in equal measure to demonstrate an observation, description, or to imitate the natural world in various ways. For instance, different mathematical shapes are often drawn, measured, developed and erected in structures such as buildings designed b architects. Moreover, the detailed maps developed through explorations have also been developed to show where humans have been before or the places they seek to visit next. Both scientific and brain researches demonstrate various learning activities which stimulate the cognitive and perceptive sections of the brain to enhance solutions for both mathematical and math problems. In fact, neurological researches have established that the neurological connections evident during math and art performances resemble one another, and both enhance neurally and brain developments (Serge, Stanislas, and Pascal). Certainly, both the visual art and math all look after perfection and beauty as the ultimate goal of understanding the concepts and precepts their success.

Studies in Euclidian and non-Euclidian geometries are among the key examples that can be used to draw the connections between mathematics and arts. The perfect connections and applications of geometry in various sciences including engineering (Wikipedia.orgs) were the motivations behind the studies in Euclidian geometries discovered around the year 300 BC when Euclid published his first book, Elements in which he postulated five key elements which describes geometry (Henrik). Euclid argued that;

- Two lines can always be joined to form a straight line
- Any straight line segment drawn can be extended to form another straight line stretching into infinity
- Provided any straight line segments, a circle can be drawn around it having the straight line as the radius of the circle as well as one end pointer of the same line as the center of the drawn circle
- All right angles in a figure are congruent to each other.
- Provided one straight line and another point not on that very line, there can be only one parallel line to the original line which goes through that particular line.

Talking about Euclidian geometry, we introduce the hyperbolic geometry which is a non-Euclidian geometry discovered by mathematicians during the 19^{th} century and which has been in use to date. The parabolic translation is formed by two circles inverted across the parallel geodesics. The intersection point for these geodesics is situated along the boundaries of the circles. Presently, the parabolic translations have been utilized in various artistic creations especially in architectural developments where the concept is applied unconsciously. Architectural designs developed in the past utilized these concepts without actually knowing their relationships with the mathematical concepts they represented (Meredith).

As opposed to mathematics, music has something to do with the emotional reactions, the feelings of life and appreciation of beauty rather than the physical calculations commonly evident in math and related subjects. As such, its connection with mathematics is somehow unimagined. Music is the most popular class of visual art in the world and which we experience or interact with in our daily lives. Despite the perceived distant relationship between music, as a form of art and mathematics, the connection is undeniably existent. Unless one accepts certain mathematical concepts in music e.g. rhythm, pitch, etc. it is very difficult to associate the cordial relationship which music and mathematics enjoy (Stepanek). The counting aspect of mathematics seems to coincide adequately with the artistic patterns of music and dance. During dancing and singing, one has to count the beats, and comply with the rhythmic patterns created for the beauty and success of the musical performance to be attained effectively (Stepanek).

Researches on the connection between music and mathematics have shown fascinating results which can be used to draw the elaborate connection between the two. For instance, researches have indicated that children who are fond of playing piano, playing soccer, or other performing art are also good in math subjects besides presenting good reasoning skills. Moreover, such children have also been shown to be very effective in solving mathematically related problems such as jigsaw puzzles, carrying out mathematical deductions and playing other calculative games such as chess (Mather). Principally, mathematics relates closely to music in three main perspectives. The first perspective related to the aspects of harmony, music tuning and tone variations in performance. The second perspective regards the presence of certain mathematical patterns in music compositions. The third perspective, on the other hands, relates to the qualities of musicians being mathematicians too. Due to these attributive connections, in some schools such as Quadrivium schools using the Pythagorean curriculum, music, astronomy, arithmetic and geometry are usually placed together in the same levels. In this classification, therefore, the creating nature evident in musical performances is totally ignored with focus laid primarily on the mathematical aspect of the performances.

The basic notion behind the classification of music alongside arithmetic is based on the knowledge of consonance and dissonance because musicians and mathematicians had realized that two different notes played together did not sound pleasant to the ear and thus lost the intended beauty associated with music (Stepanek). According to the ancient Greek musicians, philosophers, scientists and mathematicians, a single note played with a given frequency only sounded well when played with other notes whose frequencies are integers of the first. These mathematical knowledge and principles have been utilized extensively and comprehensively in musical performances to date. As Stepanek observes, the beauty of a musical performance is dependent entirely on the combination of notes, beats and rhythms successfully to coordinate well with each other. This brings out the natural beauty with which music is comprehended and appraised through the general appeals. Musical composers, therefore have to determine the best applicable notes and rhythms for their artistic works. This also enables success in the performance such as dances in these particular musical performances. This perspective of the relationship analysis relates to the fact that a lot of successful musicians are also good in mathematics or good mathematicians always make good musicians

Having highlighted the relationships between these two seemingly different yet closely related disciplines (art and math), we will analyze the relationship between the two as depicted in neurological and brain researches. This will enable a better and more comprehensive understanding and justification of the relationship in a concrete and valid manner. In this section, we shall use research experiments conducted analyzing the orientation of the brain structures and neurological components during art performances and when solving mathematically related problems and concepts. This will help to highlight the cognitive and practical relationships between music and mathematics from a practical perspective as well as from a neurological perspective. Brain analysis during art performances and mathematical solutions have shown the processing of the problems in these two disciplines to be similar in all ways. For instance, () observed that there exists a closer resemblance in the neurological processing of math and art problems in the same parts of the brain.

For instance, the study by Malkevich showed shows that the alignment characteristics and the functionality of various components of the brain portray a similar orientation when processing and analyzing the various mathematical concepts and when performing the artistic works (Geake). The study led to a conclusion that both math and art concepts are performed and analyzed in the same parts of the brain and involve the same brain components. These similarities are also observed in the unconscious use of various neurological components of the brain while performing other related artistic works such as painting dancing, sculpturing and designing architecture. All these observations send the realization that art and math are neurologically related and originate from the same part of the brain (Butterworth). Despite the observed outward dissociation, the relationship between the two principles is proven adequately in the neurological realms of understanding.

The influence of artistic performances and the performance of various mathematical concepts is a commonly noted aspect in various physical observations. Research studies analyzing the influence of mathematics on the body structures and components and the various parts of the human body that are involved in artistic performances have shown similar triggers and involvement. The parts of the body involved in any activity are controlled primarily by the CNS which controls the brain and the neurological systems to trigger movement, thinking, and reasoning. Regarding this participatory aspect, the involvement of the same body structures and components when performing mathematical and art-related activities infers that they stimulate the same features and functions of the brain, the neurological systems and the entire CNS (Marther and Loviglio). Such findings are presented in Mather and Loviglio works. According to the study, various body parts, among them the sensory systems participate in the artistic processing as well as performance. However, these processes and engagements occur unconsciously without realization by the performers or the observers. These activities are also observed when a mathematician is shaping the best aspects of their drawings or calculating the dimensions of various shapes to achieve the most accurate geometry (Marther and Loviglio). These findings further provide the proof that the connection between mathematics and art subjects/ disciplines are commonly linked and associated with one another.

In addition to the preceding studies, Serge, Stanislas and Pascal further provides an in-depth understanding of the connection between the two aspects by using the representation of parity and the number magnitudes as they are mentally conceived in the human brain. In doing these, the study timed a total of nine-odd experiments based on the Arabic and some verbal numerals to validate the connections between these two aspects. Particularly, the study looked at the mental processing of parity and numerals in the brain. The findings of this study revealed associations with the modular architecture systems regarding processing and representation of the number magnitudes and parity. For instance, Serge, Stanislas, and Pascal observed that all input numerals observed seemed to be transcoded to a common base of ten before the retrieval of parity. This infers that numerals are first processed before parities are retrieved showing the interconnectivity between the artistic and math related problems processing in the human brain, hence the validated relationship between the two.

Conclusion

To conclude art and math have been viewed as distantly related disciplines with the connection between them being close to unimaginable. Occasionally, people believe that math-related activities are rational, cognitive and left-brained while art-related activities are emotional, feelings oriented and right-brain in nature. These beliefs have led to the association of math subjects and activities with fear, dejectedness, and disinterestedness. Little do people stop to think how these two seemingly distinct areas of human knowledge are connected to one another in various aspects. A closer look at the relationships, however, points to the staunch relationship between the two: math and art in various perspectives. Particularly, the geometrical aspects of mathematics, are commonly used in artistic works such as sculpturing, architecture, etc. Moreover, the processing of mathematical concepts and aspects in the human brain has been validated through research to resemble that of art in various ways. Both are processed and analyzed in the way and involving the same brain components. Certainly, the connectivity between math and art is undeniably immense.

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