Project Description

For my project I have created a mandala garden that is both functional and aesthetically pleasing according to mathematical principles, chiefly the Fibonacci sequence. The choice to use a mandala garden was a very intentional one. The mandala has often been regarded as one of the best representations of the intersection of math, aesthetics, and art. The mandala shown here, formed by octagonal shapes and concentric circles, helps represent some of the basic mathematical principles found in nature. The mandala garden also allows for maximum space to be used in an efficient manner, as it provides pathways to access most of the garden, so that all space can be utilized. The use of the keyholes as paths within the garden is both for aesthetic and functional purposes, it allows for the entirety of the garden to be utilized as it is now accessible by path. The keyhole paths, those that lay in-between the garden beds and are ended with either triangles or circles are a common feature seen in mandala gardens because they allow the gardener to access parts of the garden not within the circular beds. (Bittman 2016).

The first produce, found in the north, or top, circular bed has sets of the “three sisters” varieties growing. The three sisters is a type of strategy for planting that includes corn, bean, and squash. The three work together to help one another in the growing process. Corn stretches tall, which creates natural forming poles for the beans. The beans help the corn because the bean plants are nitrogen fixers, which helps corn which is a shallow rooted heavy feeder. The squash plants create living mulch which helps the heavy feeding corn and also the squash plant provides shade, killing weeds as well as warning off predators with spines. The three work in harmony, and while their harmonious relationship is intriguing for the mathematical nature in which they provide shade, surface area, and moisture for one another, they are also significant for culture. The three sisters are found in many native American communities and are seen as a gift from the great spirit to sustain life on earth  (“The Three Sisters”, 2014).

The second produce bed found on the south bottom quadrant circle bed has been divided into three sections. The sections are determined by how often the produce needs to be tended to, at the front is the produce most commonly harvested and in need of the most attention. This includes daily greens such as lettuce, kale, and chard/ the second third section has plants that are harvested slightly less, but still require somewhat frequent attention, this includes vegetables like eggplant and bell peppers. The furthest third included root crops which need little attention: ie. potatoes and other roots corps. While it may seem difficult to access this third quadrant, it can also be accessed from the keyhole paths found on either side of the garden bed. 

The sunflowers and lupins were chosen to line the garden bed because they are perennial nitrogen fixers. The nitrogen fixing plants work with the bacteria in the soil and ”capture the atmospheric nitrogen and convert it to bioavailable nitrates that the plants can use to grow” (Dana 2019). Sunflowers are especially fascinating because their pattern naturally represents the Fibonacci sequence. With most sunflowers, when you count the spirals on a sunflower both clockwise and counterclockwise you will pair of numbers from the Fibonacci sequence. Most commonly is 34 and 55 or 55 and 89 spirals, but some sunflowers have 89 and 144 spirals counterclockwise and clockwise (BohannonMay). The drawing of a sunflower included in my work shows how the spiral pattern of the internal section of the sunflower actually represents a graphing of the golden ration being x=[sqrt(5)-1]/2. This naturally forming pattern is one of the best examples of how integral the principles of mathematics are in the natural formation of plants.

The flower beds in the west and east circular beds have been very intentionally planted to represent the Fibonacci sequence. The different flowers planted starting the most NW circle on the left side to the most northern circle on the right start with 2 petals, then 3, 5, 8, 13, 21, 34, and 55. Furthermore the way in which I drew the garden to have circles that go in a specific pattern are meant to represent the pattern abstractly what the Fibonacci sequence looks like graphed. The flowers include, with petal numbers: begonia (2), trillium and iris (3), buttercup (5), columbine (5), larkspur (5), delphinium (8), black eyed Susan(13) Shasta daisy (21), aster (21), gaillardia (34), pyrethrum (34), and Michaelmas daisies (55) (Knot). Together, if planted in this pattern both represent the Fibonacci sequence in their physical layout and petal amounts.

The NW outermost side of the garden has another homage to the Fibonacci sequence. It is lined with the vines of the passionflower. The passionflower which does not want direct sun will do best here, and the passionflower has in order from most inner to outer 3, 5, 55, and two sets of 5 petals as the pattern, which can be seen in my drawing. This flower is special in the way that it, although out of order, represents three of the unique numbers found in Fibonacci sequence (Iannotti 2009). Furthermore, the ratio I have used to design where my walls of passionflower vines will be is a ration of 5:3:2:1, which is also found in the Fibonacci sequence.  On the SW side of the garden there are vines for peas, I have created this in the SE quadrant because the peas need large amounts of sun (Old Farmer’s Almanac). They also create symmetry in contrast to the passionflower vines opposite of them and follow the same 5:3:2:1 ratio. While initially these may be seen as just two walls of vines, their intentionality in both symmetry, ratio, and choice of plants helps further represent the Fibonnaci sequence within my garden.

In the rest of the sections outside of the beds not covered by lupins, sunflower, passionflower, or Pease I have intentionally planted spots of clovers and alfalfas. This is because clover and alfalfa are seen as living mulch. Living mulch is classified as “Any plant that is used to cover an area of soil and adds nutrients, enhances soil porosity, decreases weeds and prevents soil erosion, among other attributes” (Libretexts 2018). Alfalfa adds nitrogen and organic matter to the soil along with Phosphorus, Potassium, Calcium, Sulfur, Magnesium, Boron, Iron, Zinc. While it may not be interlaced with the vegetables and flowers, the soil can be used for planting of potter plants and spread within the beds. White clovers are widely adapted perennial nitrogen producers with that have sallow roots mass and tough stems, helping to protects form soil erosion. These nitrogen fixers are necessary for my garden because their relationship with soil bacteria converts N2 which plants cannot use to ammonia NH3 which plants are able to use to synthesize proteins (Libretexts 2018).

The pattern of the herb spiral is meant to mimic the logarithmic spiral. For consideration it is important to note that the south is the hottest, the east dries out earlier than the west and there is wetter soil at the bottom and driest at the top. You want to put your Mediterranean herbs/herbs that like to be dry in the top of the spiral and your mint and parsley as the bottom. At the top of the herb spiral is a succulent commonly known as hens and chickens (Sempervivum tectorum) which represents a beautiful naturally formed spiral.  Hens and chickens need well drained soil and full sun, perfect for the top of the spiral (Beaulieu 2005). The herbs in the garden starting from the top and to the bottom are calendula, mint, tarragon, parsley, chives, fennel, lemon balm, lavender, basil, chamomile, sage, oregano, rosemary, lemongrass with hens and chicken (“Gaia’s Garden, Hemenway 2009”; Engels 2015). All of these herbs along with the succulent are drawn in a diagram found alongside my garden design. 

Elements of symmetry, naturally forming Fibonacci sequences, use of mandalas and keyhole bed, and herb spirals all contribute to this garden. These elements not only allow for maximum efficiency of the garden, but also create aesthetically pleasing designs. While this garden may look like another garden, upon further inspection, the choices of plants, the uses of ratios, and the formation of spirals and patterns are all paying homage to the foundations of modern mathematics, the golden ratio, the Fibonacci sequence, and the logarithmic spiral. Alongside this, this garden is also meant to honor the naturally forming mathematically principles that people find so beautiful being pattern, symmetry, and bright colors. Not only is this garden both functional and intentionally created for the purposes of a multi-beneficiary ecosystem, is also made beautiful by a rooted foundation in mathematics. 

Works Consulted

Beaulieu, David. “Sempervivum: The ‘Always Live’ Plant.” The Spruce, The Spruce, 12 May 2020,

Bittman, Erin. “Making Mandalas: the Ultimate Art-Math-Meditation Combo.” WeAreTeachers, 31 July 2017,

BohannonMay, John. “Sunflowers Show Complex Fibonacci Sequences.” Science, 9 Dec. 2017,

Dana, et al. “The Best Nitrogen Fixing Plants List for Your Garden.” Pīwakawaka Valley Homestead, 26 Apr. 2020,

Engels, Jonathon. “The Magic and Mystery of Constructing a Herb Spiral and Why Every Suburban Lawn Should Have One.” The Permaculture Research Institute, 17 Dec. 2016,

Grant, Bonnie. “What Is Living Mulch: How To Use Living Mulch As A Ground Cover.” Gardening Know How, Gardening Know How,

“How to Grow Passion Flower.” How to Grow Passion Flower, The Sunday Gardner,

Iannotti, Marie. “How to Easily Grow Exotic Passion Flowers.” The Spruce, The Spruce, 28 Sept. 2019,

Knott, R. “Fibonacci Numbers and Nature.” The Fibonacci Numbers and Golden Section in Nature – 1,

Libretexts. “31.3A: Nitrogen Fixation: Root and Bacteria Interactions.” Biology LibreTexts, Libretexts, 19 Nov. 2019,

Nationwide, SARE. “White Clover.” SARE,

Old Farmer’s Almanac. “Peas.” Old Farmer’s Almanac,

Ratnala, Sujatha. “MATHEMATICS OF A FLOWER.” Medium, Medium, 4 Feb. 2018,

Rodney. “Living Mulch: Benefits & Uses.” Traditional Gardening, 27 Jan. 2020,

Schmidt, et al. “Alfalfa Living Mulch Advances Biological Control of Soybean Aphid.” OUP Academic, Oxford University Press, 1 Apr. 2007,

“The Three Sisters.” Grow Pittsburgh, 26 Nov. 2014,

Toby, Hemenway. “Gaia’s Garden- A Guide to Home Scale Permaculture.” Permabox, Chelsea Green Publishing Company, 2009,—A-Guide-to-Home-Scale-Permaculture_by-Toby-Hemenway.pdf.

Waddington, Elizabeth. “How To Make An Herb Spiral.” Seed To Pantry School, 8 May 2020,


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