Have you ever stopped to look around and notice all the amazing shapes and patterns we see in the world around us? Mathematics forms the building blocks of the natural world and can be seen in stunning ways. Here are a few of **my favorite examples of math in nature**, but there are many other examples as well.

**The Fibonacci Sequence:**

Named for the famous mathematician, Leonardo Fibonacci, this number sequence is a simple, yet profound pattern.

Based on Fibonacci’s ‘rabbit problem,’ this sequence begins with the numbers 1 and 1, and then each subsequent number is found by adding the two previous numbers. Therefore, after 1 and 1, the next number is 2 (1+1). The next number is 3 (1+2) and then 5 (2+3) and so on.

What’s remarkable is that **the numbers in the sequence are often seen in nature**.

A few examples include the number of spirals in a pine cone, pineapple or seeds in a sunflower, or the number of petals on a flower.

The numbers in this sequence also form a a unique shape known as a Fibonacci spiral, which again, we see in nature in the form of shells and the shape of hurricanes.

**Fractals in Nature:**

Fractals are another intriguing mathematical shape that we seen in nature. A fractal is a self-similar, repeating shape, meaning the same basic shape is seen again and again in the shape itself.

In other words, if you were to zoom way in or zoom way out, the same shape is seen throughout.

Fractals make up many aspects of our world, included the leaves of ferns, tree branches, the branching of neurons in our brain, and coastlines.

Learn more about fractals and how we see and apply them in our world today at the Fractal Foundation.

**Hexagons in Nature:**

Another of nature’s geometric wonders is the hexagon. A regular hexagon has 6 sides of equal length, and this shape is seen again and again in the world around us.

The most common example of nature using hexagons is in a bee hive.

Bees build their hive using a tessellation of hexagons. But did you know that every snowflake is also in the shape of a hexagon?

We also see hexagons in the bubbles that make up a raft bubble. Although we usually think of bubbles as round, when many bubbles get pushed together on the surface of water, they take the shape of hexagons.

**Concentric Circles in Nature:**

Another common shape in nature is a set of concentric circles. Concentric means the circles all share the same center, but have different radii. This means the circles are all different sizes, one inside the other.

A common example is in the ripples of a pond when something hits the surface of the water. But we also see concentric circles in the layers of an onion and the rings of trees that form as it grows and ages.

If you live near woods, you might go looking for a fallen tree to count the rings, or look for an orb spider web, which is built with nearly perfect concentric circles.

**Math in Outer Space:**

Moving away from planet earth, we can also see many of these same mathematical features in outer space.

For instance, the shape of our galaxy is a Fibonacci spiral. The planets orbit the sun on paths that are concentric. We also see concentric circles in the rings of Saturn.

But we also see a unique symmetry in outer space that is unique (as far as scientists can tell) and that is the symmetry between the earth, moon and sun that makes a solar eclipse possible.

Every two years, the moon passes between the sun and the earth in such a way that it appears to completely cover the sun. But how is this possible when the moon is so much smaller than the sun?

*Because of math. *

You see, the moon is approximately 400 times smaller than the sun, but it is also approximately 400 times further away.

This symmetry allows for a total solar eclipse that doesn’t seem to happen on any other planet.

*Isn’t nature amazing??*

**Want to know even more about these topics and explore them more deeply with your kids?** Try my math enrichment curriculum: Math in Nature.

See what your kids will explore in this short video:

This curriculum, designed for **grades 3-6**, provides hands on lessons to look at math in the real world and also practice important math skills.

It includes **picture book lists** for each topic, a detailed **teacher manual**, **student handouts** for the lessons, **‘fun fact’ summary pages** and a list of **math art projects** to go along with each theme.

I also encourage you to grab the **FREE set of math in nature posters** to show your kids math in the real world. Use these to decorate your math space and invite discussions and excitement about the beauty of math.

Simply **enter your email below** to receive these posters. You will also receive ** a special offer for my Math in Nature curriculum**, as well as math teaching tips and other freebies and offers.

I hope this gives you some fun new math ideas to learn and explore along with your kids!

## FAQs

### What are the 5 nature of mathematics? ›

In addition to theorems and theories, mathematics offers distinctive modes of thought which are both versatile and powerful, including **modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols**.

**How is mathematics used in nature give 5 examples? ›**

A few examples include **the number of spirals in a pine cone, pineapple or seeds in a sunflower, or the number of petals on a flower**. The numbers in this sequence also form a a unique shape known as a Fibonacci spiral, which again, we see in nature in the form of shells and the shape of hurricanes.

**What are some of the great examples of math in nature? ›**

A great example of mathematical concepts in nature is symmetry which is found in abundance in the natural world. **A snowflake exhibits a six-fold radial symmetry with unique and identical patterns on each arm.**

**How is mathematics shown in nature? ›**

**Mathematics is visible everywhere in nature, even where we are not expecting it**. It can help explain the way galaxies spiral, a seashell curves, patterns replicate, and rivers bend. Even subjective emotions, like what we find beautiful, can have mathematic explanations.

**What are the 5 branches of mathematics? ›**

**The main branches of pure mathematics are:**

- Algebra.
- Geometry.
- Trigonometry.
- Calculus.
- Statistics and Probability.

**What are 5 examples of nature? ›**

Few examples of natural things are – **The moon, sun, river, clouds, mountain, rain, water** and so on.

**What are 10 examples of patterns in nature? ›**

Natural patterns include **spider webs, trees, shells, leaves, spirals, scales, meanders, waves, spots, stripes**, and many more! Do you have a favorite pattern?

**What are 5 examples of pattern? ›**

Few examples of numerical patterns are: **Even numbers pattern -: 2, 4, 6, 8, 10, 1, 14, 16, 18**, … Odd numbers pattern -: 3, 5, 7, 9, 11, 13, 15, 17, 19, … Fibonacci numbers pattern -: 1, 1, 2, 3, 5, 8 ,13, 21, … and so on.

**What are examples of math in the world? ›**

**Preparing food**. Figuring out distance, time and cost for travel. Understanding loans for cars, trucks, homes, schooling or other purposes. Understanding sports (being a player and team statistics)

**What are the 5 patterns in nature How is Fibonacci related to nature? ›**

**On many plants, the number of petals is a Fibonacci number**: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals.

### Why mathematics is important in our nature? ›

**It gives us a way to understand patterns, to quantify relationships, and to predict the future**. Math helps us understand the world — and we use the world to understand math. The world is interconnected. Everyday math shows these connections and possibilities.

**What is math in nature called? ›**

A **fractal's pattern** gets more complex as you observe it at larger scales. This example of a fractal shows simple shapes multiplying over time, yet maintaining the same pattern. Examples of fractals in nature are snowflakes, trees branching, lightning, and ferns.

**What is mathematics in nature and to the world? ›**

Mathematics in Nature is **a science and mathematics unit that allows students to explore and gain knowledge about mathematical patterns found in nature**, such as tessellations and the Fibonacci sequence. The unit also has interdisciplinary connections to other subject areas.

**What is the relationship between math and nature? ›**

Mathematics were not invented by humans, but they are a universal language. The same that uses nature to express themselves through their beings, communicate and manage the gear of each of its parts, either an atom or a galaxy, either microscopic or macroscopic.

**What is the 5 scientific method? ›**

The five steps of the scientific method include **1) defining the problem 2) making observations, 3) forming a hypothesis, 4) conducting an experiment and 5) drawing conclusions**.

**What are the five 5 major area of environmental science? ›**

These five fields are **atmospheric sciences, ecology, environmental chemistry, geosciences, and social sciences**.

**What are the 5 essential components of the scientific method? ›**

**Here are the five steps.**

- Define a Question to Investigate. As scientists conduct their research, they make observations and collect data. ...
- Make Predictions. Based on their research and observations, scientists will often come up with a hypothesis. ...
- Gather Data. ...
- Analyze the Data. ...
- Draw Conclusions.

**What are the 4 main things in math? ›**

**Addition, subtraction, division and multiplication**

Knowing these operations is essential for handling money: Addition: It involves adding two or more numbers together.

**What are the 4 things in math? ›**

Problem solving is greatly emphasized and multi-step problems can become challenging. A great way to help at home is to practice math facts daily — **adding, subtracting, multiplying, and dividing**.

**What are the five goals of mathematics? ›**

The content of the mathematics standards is intended to support the following five goals for students: becoming mathematical problem solvers, communicating mathematically, reasoning mathematically, making mathematical connections, and using mathematical representations to model and interpret practical situations.

### What are 5 ways to environment? ›

**Ten Simple Things You Can Do to Help Protect the Earth**

- Reduce, reuse, and recycle. Cut down on what you throw away. ...
- Volunteer. Volunteer for cleanups in your community. ...
- Educate. ...
- Conserve water. ...
- Choose sustainable. ...
- Shop wisely. ...
- Use long-lasting light bulbs. ...
- Plant a tree.

**What is nature simple answer? ›**

Nature refers to **all the animals, plants, and other things in the world that are not made by people, and all the events and processes that are not caused by people**. These grasses grow wild in nature.

**What are 2 examples of nature and nurture? ›**

What are some examples of nature vs. nurture? **Eye color and skin pigmentation** are examples of "nature" because they are present at birth and determined by inherited genes. Language and having a regional accent are learned after birth and occur through "nurture."

**What are the 6 patterns in nature? ›**

Natural patterns include **symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes**.

**What are the three 3 types of patterns in mathematics? ›**

There are different types of patterns in mathematics, such as number patterns, image patterns, logic patterns, word patterns, and so on. The number pattern is the most commonly used one since students are aware of even numbers, odd numbers, skip counting, etc., which help in understanding these patterns easily.

**What are the 2 types of pattern in nature? ›**

Fractals & Spirals

We see this type of pattern in trees, rivers, mountains, shells, clouds, leaves, lightning, and more. Spirals are another common pattern in nature that we see more often in living things.

**What is math pattern and give 3 examples? ›**

The sequence 0, 1, 1, 2, 3, 5, 8, 13 is the **Fibonacci pattern**. The pattern that is followed here is 0 + 1 = 1, 1 + 1 = 2 , 1 + 2 = 3 , 2 + 3 = 5, 3 + 5 = 8. The representation of the numbers in the form of an equilateral triangle arranged in a series or sequence is known as a triangular number pattern.

**What is the pattern rule in math? ›**

A pattern rule is **a mathematical relationship used to find the value of each term in a sequence**. To describe certain sequences, a pattern rule can be established. This is an algebraic equation that enables you to quickly find the value of a term in a sequence using its rank.

**What are 10 things that involve math? ›**

**10 Ways We Use Math Everyday**

- Chatting on the cell phone. Chatting on the cell phone is the way of communicating for most people nowadays. ...
- In the kitchen. Baking and cooking requires some mathematical skill as well. ...
- Gardening. ...
- Arts. ...
- Keeping a diary. ...
- Planning an outing. ...
- Banking. ...
- Planning dinner parties.

**Where is math used in the Bible? ›**

One of the greatest miracles Jesus performed on earth involved multiplication. In **Matthew 14:13–21** , Jesus multiplied five small loaves of bread and two tiny fish to feed 5,000 men. Including women and children, it's likely there were 15,000–20,000 people Jesus fed with one boy's meager lunch!

### What is math in our life? ›

Mathematics **makes our life orderly and prevents chaos**. Certain qualities that are nurtured by mathematics are the power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and even effective communication skills.

**What is the math behind the Fibonacci sequence? ›**

The sequence follows the rule that **each number is equal to the sum of the preceding two numbers**. The Fibonacci sequence begins with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ... Each number, starting with the third, adheres to the prescribed formula.

**What is the Fibonacci formula? ›**

The Fibonacci Sequence is given as: **Fibonacci Sequence = 0, 1, 1, 2, 3, 5, 8, 13, 21**, …. “3” is obtained by adding the third and fourth term (1+2) and so on. For example, the next term after 21 can be found by adding 13 and 21.

**What are some examples of Fibonacci in real life? ›**

A perfect example of this is the **nautilus shell**, whose chambers adhere to the Fibonacci sequence's logarithmic spiral almost perfectly. This famous pattern shows up everywhere in nature including flowers, pinecones, hurricanes, and even huge spiral galaxies in space.

**Does math exist in nature? ›**

Maths is innate

Shapes that can be seen repeatedly in themselves (never-ending patterns) are called Fractals. They exist in nature ranging from macroscopic to microscopic observations as rivers, coastlines, mountains, clouds, plants, snowflakes, lightning strikes, seashells and even blood vessels.

**What happen if there is no mathematics in nature? ›**

Now imagine how different our daily landscape would be if mathematics had never came to be. It would mean no time, no calendars, no buildings, no transportation, no recipes… the list goes on and on. Quite simply, **all of the comforts which make our lives what they are today would be no more**.

**How can mathematics help us control nature? ›**

Mathematics can help us control nature and occurrences in the world for our own good through **mathematical modelling**. these disasters, let alone control them or reduce the damage. prepare for untoward consequences, or better yet, maybe we can stop them from happening.

**What is the golden number in nature? ›**

The golden ratio is 1.618, represented by the Greek letter 'phi', is said to be is a mathematical connection between two aspects of an object. It is also called the Fibonacci sequence and it can be found across all of nature: **plants, animals, weather structures, star systems** – it is ever-present in the universe.

**Does math exist outside of humans? ›**

Mathematical realism, like realism in general, holds that **mathematical entities exist independently of the human mind**. Thus, humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same.

**What comes first mathematics or nature? ›**

1) **Math is innate**.

The structures of mathematics are intrinsic to nature. Moreover, if the universe disappeared tomorrow, our eternal mathematical truths would still exist.

### What are the 4 basic concepts of mathematics? ›

--**addition, subtraction, multiplication, and division**--have application even in the most advanced mathematical theories. Thus, mastering them is one of the keys to progressing in an understanding of math and, specifically, of algebra.

**What are the 4 basic mathematics? ›**

...

**The four basic arithmetic operations in Maths, for all real numbers, are:**

- Addition (Finding the Sum; '+')
- Subtraction (Finding the difference; '-')
- Multiplication (Finding the product; '×' )
- Division (Finding the quotient; '÷')

**What are the five importance of mathematics? ›**

Mathematics has a number of very useful benefits to our mind if we go into its study. It **develops our reasoning, helps us to have analytical thinking, quickens our mind, generates practicality and also its use can be applied in the day to day**. The mathematics is present in our daily lives.

**What are the 6 principles of mathematics? ›**

...

**The six Principles address overarching themes:**

- Equity. ...
- Curriculum. ...
- Teaching. ...
- Learning. ...
- Assessment. ...
- Technology.

**What are the 3 characteristics of mathematics? ›**

characteristics of the language of mathematics The language of mathematics makes it easy to express the kinds of thoughts that mathematicians like to express. It is: • **precise (able to make very fine distinctions); • concise (able to say things briefly); • powerful (able to express complex thoughts with relative ease)**.

**What math should a 8th grader know? ›**

The primary strands for an 8th-grade math curriculum are **number sense and operations, algebra, geometry, and spatial sense, measurement, and data analysis and probability**. While these math strands might surprise you, they are all critical lessons for an 8th-grade math curriculum.

**What is the most difficult math? ›**

**The Riemann Hypothesis**, famously called the holy grail of mathematics, is considered to be one of the toughest problems in all of mathematics.

**What is the easiest math to learn? ›**

Which math classes are the easiest? According to a large group of high-schoolers, the easiest math class is **Algebra 1**. That is the reason why most of the students in their freshman year end up taking Algebra 1. Following Algebra 1, Geometry is the second easiest math course in high school.

**Is basic math hard? ›**

Standard-Level and Basic-level Question papers shall be based on the same syllabus. However the Standard-Level Mathematics assesses higher Mathematical abilities compared to Basic-Level. Accordingly, **the difficulty level of the Mathematics – 'Basic' is less than that of Mathematics-'Standard'**.

**What are the 10 reasons why mathematics is important? ›**

**Here are ten reasons why math is important for kids to learn.**

- Helps Kids Develop Critical Thinking Skills. ...
- Develops a Healthy Brain. ...
- Teaches Kids How to Handle Failure. ...
- Helps Kids Understand the World Around Them. ...
- Encourages Kids to Be Creative. ...
- Teaches Kids How to Make Decisions. ...
- Boosts Self-Confidence.

### Why is math important in the real world? ›

**It gives us a way to understand patterns, to quantify relationships, and to predict the future**. Math helps us understand the world — and we use the world to understand math. The world is interconnected. Everyday math shows these connections and possibilities.

**What is a five frame in math? ›**

What are Five and Ten Frames? Five and ten frames are **equal-sized rectangular boxes in a row where each box is large enough to hold a counter**. The five frame is arranged in a 1-by-5 array. A ten frame is a set of two five frames or a 2-by-5 array.

**What are the 5 C's of mathematical engagement? ›**

Well, as Jo Boaler says, meaningful math tasks combine the 5C's: **curiosity, connection making, challenge, creativity, and collaboration**.