Have you ever played with shapes and patterns? That's what geometry is all about! It's the study of lines, angles, shapes, and space. From drawing cool designs to building structures, geometry is an important part of our world.

The overall objective of this project was to explore which shapes can (or cannot) tile a rectangular grid or infinite plane (in one or multiple ways) and understand why.

Why do bees build hexagonal honeycombs instead of square or triangular ones? This project explores which shapes can tile a flat surface without gaps and which shape uses the least material.

You build pentominoes from LEGO bricks and heptiamonds from pattern blocks. You cut wheelbarrow and kite-and-dart pairs from tagboard. Then you test whether each shape can fill a grid or cover a flat plane.

Twelve pentominoes can tile several rectangular grids. All but one of the 24 heptiamonds tile a plane on their own. Using algebra and geometry, you prove that hexagons use less wax than squares or triangles to create the same area.

Project Title: Tiling with Shapes and Tessellations in Nature

Objectives/Goals

The overall objective of this project was to explore which shapes can (or
cannot) tile a rectangular grid or
infinite plane (in one or multiple ways) and understand why.
Methods/Materials
We discovered many different types of amazing shapes that have been used in
tiling in man-made objects
such as puzzles, art, and architecture, and tessellations in nature such as
crystals and honeycombs. We
decided to experiment with the following shapes: Pentominoes, Heptiamonds,
Wheelbarrow, Kite #n#
Dart Pair, and Regular Convex Polygons (including Triangles, Squares, and
Hexagons).
We built pentominoes from legos, heptiamonds from pattern blocks; wheelbarrow
and kite #n# dart from
tagboard, and different types of (triangular, square, and hexagonal) honeycombs
with manipulatives. We
experimented tiling appropriate rectangular grids and planes using these shapes.
We used a symmetry principal to reduce the number of tiling problems for
pentominoes.
We counted the number of sides used in building honeycombs and noticed patterns
for which we derived
formulas for the amount of wax used.

Results

We found that we can tile some rectangular grids (8x8 with a square removed
anywhere, 3x20, 4x15,
5x12, and 6x10) with twelve pentominoes. Additionally, we discovered that all
but one of the 24
heptiamonds could tile a plane individually. We invented interesting,
non-trivial ways of tiling a plane
using both wheelbarrow and kite #n#dart pairs. Finally, we used manipulatives,
algebra, and geometry to
prove that hexagons are the most efficient shape (consume the least wax to
create the same amount of
area) from all regular convex shapes to build a honeycomb.

Conclusions/Discussion

We discovered that although many different types of convex and non-convex shapes
(e.g. pentominoes,
wheelbarrow) and several interesting combinations of them (e.g. kite n#dart) can
be used to tile a plane in
interesting ways, there are many simple shapes that cannot be used to tile the
plane (e.g. a V-shaped
heptiamond or a pentagon). Although we proved that hexagons use the least amount
of wax in comparison
to squares or triangles, we did not prove that they are better than irregular or
multiple shapes to hold
honey (we discovered that the general proof was given only five years ago in
1999!).

Summary Statement

In this project we explored which shapes can or cannot tile an infinite plane or
rectangular grid, explained
why, and applied our findings to nature and society.



Tiling Patterns and Honeycomb Efficiency

Which shapes can tile an infinite plane?

<h1><strong>1000 Science Fair Project Ideas by Subject</strong></h1><p>Looking for a science fair project idea? Each of our science fair project idea has complete instructions with video. Get ideas for your science projects, find extra resources for your class' scientific projects, or try a fun experiment at home! It doesn't matter what grade you're in, there's something for everyone!</p><p>You can find your perfect science fair project from the different science subjects below or from our <a href="https://www.all-science-fair-projects.com/category0.html#bottom">science fair project idea lists!</a></p>

<h2>Science Fair Project Idea Lists</h2><p>Looking for other ways to find good ideas for science fair projects? Check out these lists of science projects!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3>Easy Science Fair Projects</h3><p><img src="/images2/flex/176_popular 2 (2).png" data-size="100" data-float="left" style="width:100px; float:left">Explore the exciting world of science with an easy science fair project that you can do at home using simple materials. Any one of these easy project ideas will teach you important scientific concepts and help you have fun while learning. An easy science fair project is a great way to introduce the wonders of science to kids and adults alike!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><ul><li><p>Changing the Color of Flowers</p></li><li><p>Baking Soda Volcano</p></li><li><p>Swimming Raisins</p></li><li><p>Egg in Vinegar</p></li><li><p>Color of Skittles Experiment</p></li><li><p>Jumping Rice Krispies</p></li><li><p>Mixing Colors of Light</p></li><li><p>Camouflage and Hide</p></li><li><p>Light and Dark on Seed Germination</p></li><li><p>Make a Parachute</p></li></ul><p>More science project details at <a href="https://www.all-science-fair-projects.com/science_fair_project_list/12">Easy Science Fair Projects <strong>→</strong></a></p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3>The Top 10 Best Science Fair Projects</h3><p><img src="/images2/flex/177_popular 2 (3).png" data-size="100" data-float="left" style="width:100px; float:left">To find the best science fair project for you, we've picked the best science projects from 10 different science categories, all with very interesting topics. If you're looking for more science projects at another difficulty level or topic, you can explore science fair project ideas by grade level at the top of this page!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><ul><li><p>Jet Lag in Hamsters (circadian rhythm, Biology science fair project)</p></li><li><p>Egg with Vinegar (acid-base reaction, Chemistry science fair project)</p></li><li><p>Galileo's Inclined Plane Experiment (acceleration, Physics science fair project)</p></li><li><p>Plant's Favorite Color for Photosynthesis (Photosynthesis, Botany science fair project)</p></li><li><p>Color and Taste (color perception, Psychology science fair project)</p></li><li><p>Does Dog Saliva Kill Bacteria? (antibacterial, Microbiology science fair project)</p></li><li><p>Decomposing Plastic Spoons (biodegradable materials, Environmental Science science fair project)</p></li><li><p>Super Hero Egg Shells (structural engineering, Engineering science fair project)</p></li><li><p>Music Math: Playing Notes with Equations (music, Math science fair project)</p></li><li><p>Temperature's Effect on Seawater (climate change, Earth Science science fair project)</p></li></ul><p>More science project details at <a href="https://www.all-science-fair-projects.com/science_fair_project_list/13">Best Science Fair Projects <strong>→</strong></a></p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3>Cool Science Fair Projects</h3><p><img src="/images2/flex/178_popular 2.png" data-size="100" data-float="left" style="width:100px; float:left">Get ready to be amazed by super cool science projects that you can do right at home! With just a few simple things, you can be fascinated by science and have tons of fun with these popular science projects!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><ul><li><p>Explosive Elephant Toothpaste</p></li><li><p>Egg in Vinegar</p></li><li><p>Electrifying Lemon Battery</p></li><li><p>Making Oobleck: Liquid or Solid?</p></li><li><p>Egg Drop Project</p></li><li><p>Colors of Skittles Experiment</p></li><li><p>Cloud in a Bottle</p></li><li><p>Baking Soda Volcano</p></li><li><p>Egg in a Bottle</p></li><li><p>Plastic Milk</p></li></ul><p>Project details and more cool science projects at <a href="https://www.all-science-fair-projects.com/science_fair_project_list/1/Popular_Science_Experiments_At_Home">Popular Science Fair Projects <strong>→</strong></a></p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3>One-Day Science Fair Project Ideas</h3><p><img src="/images2/flex/172_popular 2 (1).png" data-size="100" data-float="left" style="width:100px; float:left">Quick experiments can be a great option for a science fair project. In this list, we've highlighted one-day science fair project ideas for elementary school (easy), middle school (medium), or high school (hard). These experiments are fast and easy to do, but the science topic packs a punch!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h4>Acid-base reactions: Mixing acids with bases quickly makes carbon dioxide gas!</h4><ul><li><p><a href="https://www.all-science-fair-projects.com/project830.html"><strong>Rocket Film Canisters (easy) </strong></a>Make a rocket fly sky high with just baking soda and vinegar!</p></li><li><p><a href="https://www.all-science-fair-projects.com/project829.html"><strong>Make Your Own PH Indicator (medium) </strong></a>Learn how to make your own acid-base indicator using red cabbage and use it to test different fluids!</p></li><li><p><a href="https://www.all-science-fair-projects.com/project1327.html"><strong>Testing Antacids (hard) </strong></a>Find out which antacid can neutralize the most acid and get relief from heartburn and gastritis!</p></li></ul><h4>Chromatography reactions: Separating out colors as liquid moves through the paper!</h4><ul><li><p><a href="https://www.all-science-fair-projects.com/project826.html"><strong>Colors of Skittles Experiment (easy) </strong></a>Did you know that some Skittles have a secret rainbow hiding inside them?</p></li><li><p><a href="https://www.all-science-fair-projects.com/project678.html"><strong>Uncovering Fall Colors (medium) </strong></a>Have you ever wondered why leaves change color in the fall? Let's find out by using chromatography to separate the colors of a green leaf!</p></li></ul><h4>Heat reactions: Heat speeds things up!</h4><ul><li><p><a href="https://www.all-science-fair-projects.com/project274.html"><strong>Which Candle Burns the Fastest? (easy) </strong></a>Do you want to find out which color candle burns the fastest?</p></li><li><p><a href="https://www.all-science-fair-projects.com/project1291.html"><strong>Fire-Resistant Balloons (medium) </strong></a>Ever wondered if a balloon filled with water can withstand fire?</p></li><li><p><a href="https://www.all-science-fair-projects.com/project475.html"><strong>Can Peanuts Heat Water? (hard) </strong></a>Have you ever wondered if peanuts have enough energy to heat up water?</p></li></ul><p>Project details at <a href="https://www.all-science-fair-projects.com/science_fair_project_list/15/Quick_Science_Fair_Projects_You_Can_Do_In_A_Day">Quick Science Fair Projects →</a></p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3 style="text-align: start"><strong>Testable Questions for Science Projects</strong></h3><p><img src="/images2/flex/173_popular 2.png" data-size="100" data-float="left" style="width:100px; float:left">A testable question is a question that we can answer through a science experiment. To do this, we do a control experiment, then we change one thing in the experiment to see how it affects what happens. This is how we can discover the answer to our question!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><ul><li><p>What makes a cloud form?</p></li><li><p>Can drink and food taste different just by changing its color?</p></li><li><p>Does the color of light affect photosynthesis?</p></li><li><p>Does temperature affect seed sprouting?</p></li><li><p>What makes popcorn pop?</p></li></ul><p>More <a href="https://www.all-science-fair-projects.com/science_fair_project_list/14">testable questions with their science projects <strong>→</strong></a></p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h2>Science Fair Project FAQ</h2><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3>What are some hands-on ways to find inspiration for my science fair project?</h3><h4>Science museums</h4><p><img src="/images2/flex/124_7.png" data-size="100" data-float="left" style="width:100px; float:left">Science museums are great places to explore if you're looking for inspiration for your next science fair project or just want to learn more about science. Science museums, natural history museums, space museums, and discovery museums are all great places to do that! You can discover all sorts of interesting things about science and find cool project ideas for science fairs.</p><p>There may be free admission days or free passes to a science museum near you! Check your credit card for offers, your local library for free museum passes, and nearby science museums for free entrance days.</p><p>So what are you waiting for? <a href="https://en.wikipedia.org/wiki/List_of_science_museums">Find a science museum near you</a> and prepare to be awed by all that you can learn there!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h4>Look around and observe</h4><p><img src="/images2/flex/117_5.png" data-size="100" data-float="left" style="width:100px; float:left">Do you know how scientists start their cool projects? They often look around and notice things that are interesting or make them curious. Then they start doing an experiment! You can do the same! Look around your school, home, or community. Is there anything that catches your attention and makes you curious? Maybe you notice something interesting or a problem that people are facing. This could be a great starting point for your science fair project!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h4>Try an Easy Science Project!</h4><p><img src="/images2/flex/144_easy square.png" data-size="100" data-float="left" style="width:100px; float:left">These science projects are easy and fun to do. You may discover a simple experiment that sparks your interest and inspires you to do more experiments, turning it into a science fair project! Check them out at <a href="https://www.all-science-fair-projects.com/science_fair_project_list/12">Easy Science Fair Projects <strong>→</strong></a></p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3 style="text-align: start"><strong>How do I start a science fair project?</strong></h3><p><img src="/images2/flex/199_science coach.png" data-size="100" data-float="left" style="width:100px; float:left">No matter if you're in high school, elementary or middle school, science fair projects are a fun and unique way to discover science by asking a question and doing a science project. We'll help you find a science fair project idea and guide you through the process of doing and presenting your science fair project with <a href="https://www.all-science-fair-projects.com/science_fair_projects_coach/science-project-coach.html">Science Fair Coach's Science Fair Project Guide</a>.</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3>What should I do after I have a science fair project idea?</h3><p><img src="/images2/flex/143_intro science fair.png" data-size="100" data-float="left" style="width:100px; float:left">If you have a science fair project idea, Science Fair Coach can help you turn it into a full science fair project! Starting at the <a href="https://www.all-science-fair-projects.com/pgpage/4">Introduction to Science Fairs</a>, check out the section on <strong>How to do a science fair project</strong> for a step-by-step guide!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><p><img src="/images2/flex/203_compared to scientific method.png" data-size="100" data-float="left" style="width:100px; float:left">We'll guide you through every step of the <a href="https://www.all-science-fair-projects.com/pgpage/5">scientific method</a>, from designing and conducting your experiment to collecting and analyzing your findings.</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><p><img src="/images2/flex/202_engineering design process.png" data-size="100" data-float="left" style="width:100px; float:left">If you're working on an engineering project, you can head over to <a href="https://www.all-science-fair-projects.com/pgpage/9">The Guide to the Engineering Design Process</a>.</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><p> <img src="/images2/flex/150_science fair poster.png" data-size="100" data-float="left" style="width:100px; float:left">Finally, we'll help you showcase your results on a <a href="https://www.all-science-fair-projects.com/pgpage/7">science fair board</a> for others to learn from and enjoy.</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3 style="text-align: start"><strong>How do I make a science fair board?</strong></h3><p style="text-align: start"><img src="/images2/flex/150_science fair poster.png" data-size="100" data-float="left" style="width:100px; float:left">Your science fair board is where you show off your science fair project for everyone to see and learn from. With <a href="https://www.all-science-fair-projects.com/science_fair_projects_coach/science-project-display-board-6a.html">Science Fair Coach's step-by-step guide</a>, you can make sure your science fair board stands out and impresses at the science fair!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><hr style="clear:both; border-style:dotted" data-marker="clearFloat"><h3>Where can I find a science fair competition?</h3><p><img src="/images2/flex/179_Intro Science Fair Projects 32.png" data-size="100" data-float="left" style="width:100px; float:left">Science fair competitions are an excellent opportunity to explore science. One of the of the premier science advocacy organizations, the Society for Science, is associated with more than 400 science fair competitions in almost every US state, as well as over 70 other countries, regions, and territories. You can find out if there's a <a href="https://findafair.societyforscience.org/">Society of Science affiliated science fair</a> near you!</p><p>The <a href="http://physics.usc.edu/~gould/ScienceFairs/">The www Virtual Library: Science Fairs website</a> also has a collection of science fairs from all over the world, as well as national, state, regional, local, and virtual competitions!</p><hr style="clear:both; border-style:dotted" data-marker="clearFloat">

Math is all about numbers, patterns, and solving problems. Computer science is about using math and technology to create computer programs and solve real-world problems. Together, they help us understand how things work, how to solve problems, and how to use technology to make our lives better!

All Science Fair Projects

1000 Science Fair Projects with Complete Instructions

Tiling Patterns and Honeycomb Efficiency

Hypothesis

Method & Materials

Results

Why do this project?

Also Consider

Full project details

Related Science Fair Project Ideas