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What is Geometry? – Chloe Lin
You may have a vague idea about geometry, but have never really understood it fully. So let’s explore the topic of geometry a bit more.
What actually is geometry? Our world has lots of geometry incorporated into it. From fascinating architecture, the shape of a soccer ball, to the study of shapes, geometry is hidden everywhere in your everyday life. Geometry is a branch of mathematics and works with the shapes of objects and their connections to other objects, such as how triangles and squares form the basis of a building. If you’re wondering where the word geometry came from, it actually originated from the Greek-words meaning “Earth Measurement”. Many people eventually realized that geometry doesn’t need to be limited to just the study of 2D and 3D objects but can also expand into other more abstract ideas or different concepts such as more modern art or using geometry in many ways!
The earliest form of geometry was in ancient Egypt and Mesopotamia, where they started figuring out what techniques to use to better understand land and create buildings. Nowadays, geometry is also used for CG animation, using points and vectors to create realistic 3D models. Learning more about geometry can benefit your understanding and knowledge of it and can be very useful in the future!
The Latest News! – Allison Lin
A tetrahedron is a 3D shape with 4 triangular faces and 6 edges. Tetrahedrons are similar to pyramids, but with one less side. In 1966, John Conway and Richard Guy started wondering about the balance of a tetrahedron. They wanted to know if a tetrahedron with an evenly distributed weight could be made to only balance on one side. After many attempts, the two eventually decided it was impossible. If the shape had an uneven weight distribution, it should be an easy question, solved by putting a heavier weight on one side.
However, this solution is only sustainable for shapes with rounded edges. In 2006, Hungarian mathematician and engineer Gábor Domokos approached the problem, having experiences in balance, discovered a shape called a gömböc, which is something that only balances on two points (one stable and one unstable) like a coin.
In 2023, Domokos and his students Dawson and Almádi discovered that in theory, a tetrahedron could be constructed with a specific weight distribution so that it only balances on one side.
On June 24, 2025, Almádi was able to use computer 3D models to create a tetrahedron that is monostable(a 3D shape that only balances on one side), always flipping to the same side no matter how it is put down. This geometric wonder is only made possible by a tetrahedron made up of obtuse triangles, which distributed the weight just enough for the shape to always flip to one side. The weight is added to one small portion of a side of the obtuse triangle, which explains the logic behind how the shape can be monostable.
Fun Facts! – Chloe Hsu
There are many fun facts about geometry which some also relate to everyday activities!
- To start off, the word Geometry comes from the Greek word “Earth” and measures
- The regular soccer ball is made up of 32 shapes, 12 pentagons and 20 hexagons
- All triangles’ interior angles add up to be 180 degrees
- Have you noticed that the opposite sides of a die add up to 7?
- Many people disagree on how to cut sandwiches, but cutting a sandwich diagonally is actually more common than cutting it vertically
- The ratio of a circles’ circumference to diameter is always pi (3.14)
- The hour and minute hands of a clock meet at 90 degrees 44 times in a day
- There are 43252003274489856000 ways to solve a rubik’s cube
- Pizzas are often round so that the cooking is even in the round oven
History – Romero Santiago
Geometry was considered to be one of the two big pre-modern parts of math, the other being arithmetic. Geometric formulas and rules were being used and discovered all the way back in 3000 BCE with the Egyptians, who used and came up with a lot of them, like one to find the area of a circle. Babylonian mathematicians were the first people to come up with the mathematical constant, pi (π), a number used to figure out certain qualities of circles.
The Greeks played a huge role in the history of geometry. In 300 BCE, a Greek scholar known as Euclid released a book known as ‘Elements’. This was his collection of geometric theorems and formulas, and for a long time to come, Elements would be used as the go-to geometry textbook for students around the world. The golden ratio was first defined in this book, which is a number that appears a lot in nature and was innovated by the Greeks to create buildings that looked good and were visually pleasing. Pythagoras, another famous mathematician, came up with his famous ‘Pythagorean theorem’ regarding the sides of right triangles, which are triangles that have a 90° angle in them. Finally, Archimedes found out ways of finding the volume of pretty much all 3D shapes.
Modern geometry was started by the findings of René Descartes. He came up with analytical geometry, which is the process of using points and lines on a graph to make shapes and coming up with rules about the shapes made on said graphs. Nowadays, we are at the point where mathematicians are coming up with theories saying that there may be shapes that don’t exactly follow all these rules that have been come up with over the years and are trying to come up with formulas for them, such as in hyperbolic and spherical formulas.
Career – Xinye Zhu
There are so many opportunities to get involved with geometry, and options to possibly pursue it as a career! Geometry can be found and used in many unassuming jobs. For example, if you enjoy mathematics and educating peers and the community, then maybe a career as a math teacher interests you, as you are able to incorporate math and geometry into what you’re employed to do daily.
And again, some careers, such as urban planners or architects, require the knowledge of geometry to safely strategize how to construct most things, from skyscrapers to your classic suburban home. In the future, architects will find themselves innovating to create more sought-after constructions.
For anyone who wishes to become an artist or pursue a career path in the creative space, then animation and animating might be just what you’re looking for! Animators and geometry work hand in hand– animation and cartoon require the use of this work to create proportional lines and objects. Perspective art– a style in which artists use 3D-inspired shapes and figures to create illusions in their drawings– also heavily relies on geometry to accurately portray a scene that everyone can understand.
There are so many more careers in which geometry is used and required, almost endless opportunities; the study of geometry is extremely flexible. From construction workers who built the houses and structures you see, to the interior designers who decorated those houses, geometry can be found everywhere, and everyone interacts with the direct result on a daily basis. The career options are vast and all incredibly unique; there’s room for everyone!
What Does this Have to Do With Me? – Charis Tsang
Geometry is all around us, even if we don’t always notice it. In architecture, it helps design buildings with the right proportions, dimensions, and angles so they are safe and beautiful. An example would be the Louvre Pyramid in Paris which uses triangles and symmetry to create a modern glass structure that fits perfectly with the historic museum. Interior design and environmental planning also use geometry to arrange spaces in ways that are comfortable and useful. We use geometry in daily life too! When reading maps, choosing routes, or measuring distances, we are using geometry without even thinking about it. It also shows up in cooking, baking and crafting, where we need exact measurements and angles to make sure things fit together just right. Geometry is even part of fun things we enjoy, such as video games, robotics, arts, and sports! It helps create movement, balance and design.
Did you know that nature also follows geometry? Bees make honeycombs in perfect hexagons, snail shells grow in spirals, and trees branch out in patterns that help them grow. Snowflakes, flower petals, and the human body all demonstrate amazing geometric patterns. Learning geometry matters because it’s a key part of technology, design, and problem solving, and it helps us understand the hidden pattern that shapes our world.
BONUS QUIZ! – Weiyu Tsay
- Geometry in Greek means _________
2. Where was the earliest form of geometry found in?
a) Egypt and Mesopotamia
b)China and Mongolia
c) California and Oregon
d) Michigan and Ohio
3. How many faces does a tetrahedron have?
a) 3
b) 16
c) 10
d) 4
4. Pi is the ____ of a circles’circumference to diameter
5. What was the book that Euclid wrote called?
a) Avatar
b) Elements
c) The geometry textbook
d) Geometry
6. bWhat job can you do with geometry if you like art?
7. True or false, geometry cannot be found in nature.
Did you get them all right? See how you did below the FAQ!
FAQ on Geometry – Weiyu Tsai
What does the π symbol mean?
This weird but cool looking symbol, π, is called pi, and it’s pronounced just like how you would pronounce the pie that you eat on thanksgiving. This symbol is the ratio of the circumference of a circle to the diameter. There are a lot of big words. A circumference is the outer circle, so how much rope you need to wrap the entire circle. The length of the would be the circumference. The diameter is how long a rope that goes from one side of the circle to the opposite side is. So every time you divide the circumference by the diameter, you will always get π. This ratio, the number you get when you divide the circumference by the diameter, is around 3.14, but it is an irrational number, meaning it goes on forever. There is no end to π. There are even competitions where people try to say the most digits in pi. Check out: https://www.piday.org/million/. if you want to see more digits of pi.
What are the answers to the quiz?
- Earth measurements 2. A 3. 4 4. Ratio 5. B 6. Animation and animating 7. False
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