A

 Abscissa the x-coordinate of a point: its distance from the y-axis measured parallel to the x-axis Absolute temperature the scale of temperature measuring thermodynamic activity (molecules) in the substance from none (absolute zero), when nothing is moving and scale moves upward, uses the system of Kelvin Accurate free from error due to careful measurements Acute triangle a triangle with internal angles that are smaller than 90° (three acute angles) Ahmes was an Egyptian scribe who lived around 1680-1620 BC and worked with mathematics Alchemists a person who practices alchemy Alchemy In the history of science, alchemy refers to both an early form of the investigation of nature and an early philosophical and spiritual discipline, both combining elements of chemistry, metallurgy (Study of metals), physics, medicine, astrology, semiotics (Study of signs and symbols), mysticism, spiritualism, and art all as parts of one greater force. Alchemy has been practiced in Mesopotamia, Ancient Egypt, Persia, India, and China, in Classical Greece and Rome, in Muslim civilization, and then in Europe up to the 19th century. Algebra statements of relations of numbers using symbols and letters to represent values Analytic geometry a branch of mathematics in which algebraic procedures are applied to geometry and position is represented analytically by coordinates. Also called coordinate geometry. Angles the shape created when two lines meet Aperiodic non repeating pattern in tiling Arbitrary a measurement that could vary based on convenience, location Archimedes an ancient Greek mathematician, physicist, engineer, astronomer, and philosopher. Aristotle a Greek philosopher, a student of Plato and teacher of Alexander the Great. He wrote on diverse subjects, including physics, metaphysics, poetry (including theater), biology and zoology, logic, rhetoric, politics, government, and ethics. Along with Socrates and Plato, Aristotle was one of the most influential of the ancient Greek philosophers. Assets In business and accounting an asset is any economic resource controlled by an entity as a result of past transactions or events and from which future economic benefits may be obtained. Examples include cash, equipment, buildings, and land. Asymmetrical the absence of, or a violation of, a symmetry Atomist Theory any theory in which all matter is composed of tiny discrete finite indivisible indestructible particles; "the ancient Greek philosophers Democritus and Epicurus held atomic theories of the universe" Azimuth angle from the horizon  toward the zenith (directly above)

B

 Babylonians the ancient peoples who lived between the Tigris and Euphrates rivers (present day Iraq), a state in southern Mesopotamia Bar graph a chart with rectangular bars of lengths usually proportional to the magnitudes or frequencies of what they represent. Bar charts are used for comparing two or more values. The bars can be horizontally or vertically oriented. Base 60 a unit divided up into sixty equal fractions as in an hour having 60 minutes. Bilateral symmetry division of an organism into roughly mirror image halves (with respect to external appearance only); reflection symmetry. Bose, Satyendra a Bengali Indian physicist, specializing in mathematical physics. He is best known for his work on quantum mechanics in the early 1920s, providing the foundation for Bose-Einstein statistics and the theory of the Bose-Einstein condensate. He is honored as the namesake of the boson. Bose-Einstein Condensate a state of matter that forms below a critical temperature in which all bosons that comprise the matter fall into the same quantum state Brainstorm to try to solve a problem by thinking intensely about it

C

 Calculus a field of mathematics that builds on analytical geometry that can help you look a either extremely large numbers or very small ones. Calibration making equipment measure the exact same amount for scientific purposes. Capacity the amount a container can hold Cardinal numbers a number that states how many items are in a group Cartesian coordinates In mathematics, the Cartesian coordinate system is used to determine each point uniquely in a plane through two numbers, usually called the x-coordinate and the y-coordinate of the point. To define the coordinates, two perpendicular lines (the x-axis and the y-axis), are specified, as well as the unit length, which is marked off on the two axes. Cartesian coordinate systems are also used in space. Cartography Cartography or mapmaking is the study and practice of making maps or globes. Chaos theory the theory that very small changes in a system can lead to the seemingly random nature of the result this is caused by high error in calculations Charts a picture used to display data. Circumference the measurement of the perimeter of a circle Clepsydra A clepsydra is a vessel with a hole in the bottom and one on the top. Colloidal suspension a colloid or colloidal dispersion is a substance with components of one or two phases. A colloid mixture is a heterogeneous mixture where very small particles of one substance are distributed evenly throughout another substance. The dispersed phase particles are largely affected by the surface chemistry existent in the colloid. Many familiar substances, including butter, milk, cream, aerosols (fog, smog, and smoke), asphalt, inks, paints, glues, and sea foam are colloids Compass a tool used to create circles with a central pivot and a drawing point. Compounds a substance consisting of two or more different chemically bonded elements Conversions the mathematical formula used to change from one unit (or system) of measurement to another Cornell, Eric a physicist who, along with Carl E. Wieman, was able to synthesize the first Bose-Einstein condensate in 1995. For their efforts, Cornell, Wieman, and Wolfgang Ketterle shared the Nobel Prize in Physics in 2001. Crystallographers a person who studies or practices the science dealing with crystallization and the forms and structure of crystals. Cube or Hexahedron a three dimensional shape formed by the joining of 6 equal squares to form a box Cubic units measurement of objects using length, width and height Cubic the cubic crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in metallic crystals Cubit the measurement from the elbow to the tip or the middle finger used in ancient times. Curves Smooth gradual bends in a line.

D

 da Vinci,  Leonardo an Italian scientist, mathematician, engineer, inventor, painter, sculptor, architect, musician, and writer. His most famous works include The Last Supper and the Mona Lisa. His drawings referred to as the secto aurea or the golden section are contained in Luca Pacioli’s work on Divina Proportions. Degree a unit of temperature, or 1/360 of a circle Democritus Democritus was a pre-Socratic Greek philosopher. Democritus was a student of Leucippus and co-originator of the belief that all matter is made up of various imperishable, indivisible elements which he called atoma or "indivisible units", from which we get the English word atom. It is virtually impossible to tell which of these ideas were unique to Democritus and which are attributable to Leucippus. Denominator the part of a fraction below the line, the number of times it splits Dependent variable are the values, i.e. the "output", of the function. The dependent variable depends on the independent variables. Descartes, Rene a highly influential French philosopher, mathematician, scientist, and writer. Dubbed the "Founder of Modern Philosophy", and the "Father of Modern Mathematics" While sick in bed he looked at the tiled ceiling and tried to track the fly by using a coordinate system. His work influenced analytic geometry, calculus, and cartography. Design an outline, sketch, or plan, as of the form and structure of a work of art, an edifice, or a machine to be executed or constructed. Diameter the measurement from the longest part of a circle from one side to the other Divisibility ability to be divided evenly Dodecahedron a three dimensional shape made using 12 faces Dyne the amount of force needed to move 1 gram of an object 1 centimeter per second squared

E

 Economists An economist is an individual who studies, develops, and applies theories and concepts from economics, and who writes about economic policy. Egyptians the inhabitants of Egypt Einstein,  Albert A German-born theoretical physicist. While best known for the theory of relativity (and specifically mass-energy equivalence, E = mc2), he was awarded the 1921 Nobel Prize in Physics. Elements A chemical element, or element for short, is a type of atom that is defined by its atomic number; that is, by the number of protons in its nucleus. The term is also used to refer to a pure chemical substance composed of atoms with the same number of protons. Empedocles a Greek pre-Socratic philosopher and a citizen of Agrigentum, a Greek colony in Sicily. Empedocles' philosophy is best known for being the origin of the cosmogenic theory of the four classical elements (Earth, air, fire, and water.) English system units of measurement on the base 12 system (inches, feet, yard, mile, etc) Equations a statement of the equality of two or more mathematical expressions Equidistant a point on a line that has the same distance from each end or another part of the line Equilateral triangle a three sided figure where all three sides and angles are equal. Euclid a Greek mathematician who lived in Alexandria, Egypt around 300BC Experiments a set of actions and observations, performed in the context of solving a particular problem or question.

F

 Fibonacci number a number in the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…..) Fibonacci an Italian mathematician of the Middle Ages Five-fold symmetry the division of an object into five equivalent parts Formula a rule or expression shown in mathematical symbols Four-fold symmetry the division of an object into four equivalent parts Fractal a geometric pattern repeated at smaller and smaller scales to form irregular shapes and surfaces that do not look like the original pattern Fractal Equations an equation that patterns a fractal Friction the resistance between two touching objects that can produce heat

G

 Gas a substance possessing perfect molecular mobility and the property of indefinite expansion, as opposed to a solid or liquid. Geometry the branch of math that looks at the measurement of shapes and how they work together Global Position System GPS uses the Cartesian Coordinate System to find reference points to compare on a worldwide grid using satellites to find a point Golden Ratio the special ratio between two quantities where their ratio is equal to their sum divided by the larger number Grams the mass of 1 cubic centimeter of water at 4 degrees Celsius Graph diagram that shows how two sets of numbers are related Gravitational attraction the amount of pull a large body, such as the earth, has on a smaller body, like a person, on or near its surface

H

 Hexagonal symmetry the division of an object into six roughly equal parts Hexagonal in geometry, a hexagon is a polygon with six edges and six vertices. The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120° and the hexagon has 720 degrees. It has 6 lines of symmetry. Hooke,  Robert an English physicist and mathematician who played an important role in the scientific revolution, through both experimental and theoretical work. Hooke's Law the linear change in tension with extension in an elastic spring

I

 Icosahedron a three dimensional shape made using 20 faces Imperial system the units of measurement used in the English colonies around the world during the 1800’s (also called the English system) Independent variable in mathematics, an independent variable is any of the arguments, i.e. "inputs", to a function. Indivisible Incapable of being divided without a remainder Inertia the amount of energy needed to make an object move Integral calculus a branch of calculus that focuses on figuring out the area and volume of irregular shapes Irrational a number that extends out to infinity and cannot be represented by a fraction Isosceles triangle at least two sides are of equal length. An isosceles triangle also has two congruent (or same) angles (namely, the angles opposite the congruent sides). An equilateral triangle is also an isosceles triangle, but not all isosceles triangles are equilateral triangles.

J

K

 Kilogram 1,000 grams the basic unit of mass in the metric system Koch snowflake one of the earliest fractals described that begins with a triangle and uses repeating smaller scale triangles around the perimeter.

L

 Lambert , Johann a German mathematician, physicist and astronomer, who in 1768 discovered pi has an infinite number of digits Law of Buoyancy also called Archimedes’ principle buoyancy is the upward force on an object produced by the surrounding fluid (i.e., a liquid or a gas) in which it is fully or partially immersed, due to the pressure difference of the fluid between the top and bottom of the object. Leucippus Leucippus was among the earliest philosophers of atomism, the idea that everything is composed entirely of various imperishable, indivisible elements called atoms. Line graph a diagram of lines made by connected data points which represent successive changes in the value of a variable quantity or quantities. Linear geometry looking at how angles and basic two dimensional shapes measure Linear systems simple modeling without changing variables Linear measurement in a single dimension along a line such as height, length or width Liters the metric unit for volume equal to 1 cubic decimeter Logic the system of principles used in any science to make sense of information. Logical proof by applying scientific and mathematic knowledge Lorenz, Edward an American mathematician and meteorologist born in 1917 who pioneered chaos theory Lucas, Eduardo a French mathematician who studied the Fibonacci sequence and determined a formula for finding a given number in the sequence

M

 Mandelbrot set the complex numbers that when put into a given equation have a boundary of a particular pattern Margin of error a statistic used to say how close a calculation is to the predicted value by a certain percentage Mass The amount of matter and energy in an object Mathematicians a specialist or expert in math Matter the substance of which physical objects are composed. It constitutes the observable Universe. There is a tendency to regard manifestations of energy, such as light and sound, as not being material. However in physics the distinction is difficult to enforce — according to the theory of relativity matter and energy can be converted to one another. Matter is said to have mass and to occupy space, but there are technical problems in physics with both criteria. Mediterranean the land surrounding the Mediterranean Sea including the southern part of Europe and the northern part of Africa Meniscus is the curvature of the surface of water when measuring with a graduated cylinders- a tall tube with markings to accurately measure volume Mesopotamia an ancient region of southwest Asia between the Tigris and Euphrates rivers in modern-day Iraq. Meter the base unit of length in the metric system ~ 39.37 inches Metric system the first standardized system of measurement created in the1790’s all units evenly divisible by 10 Metrology the science of weights and measures Middle Ages formed the middle period in a traditional schematic division of European history into three "ages": the classical civilization of Antiquity, the Middle Ages and Modern Times. It was a period of great cultural, political, and economic change in Europe typically dated from around 500 AD to approximately 1500 AD. The Middle Ages witnessed the first sustained urbanization of northern and western Europe. Modern European states owe their origins to the Middle Ages, and their political boundaries as we know them are essentially the result of the military and dynastic achievements in this tumultuous period. Milliliters 1/1000 liter equal to a cubic centimeter Mirror symmetry one side looks like the other;  bilateral symmetry or reflective symmetry Mitchell Fergenbaum a Canadian mathematician born in 1944 who worked with fractals Modeling to design or copy a problem to predict its outcome Models a pattern, plan, representation, or description designed to show the structure or workings of an object, system, or concept. Money economics offers various definitions for money, though it is now commonly defined as any good or token that functions as a medium of exchange that is socially and legally accepted in payment for goods and services and in settlement of debts. Money also serves as a standard of value for measuring the relative worth of different goods and services. Monoclinic in crystallography, the monoclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. They form a rectangular prism with a parallelogram as base. Hence two pairs of vectors are perpendicular, while the third pair make an angle other than 90°.

N

 Negative numbers a positive number is a number that is less than zero. On a number line all positive numbers are always to the left. Newton, Sir Isaac an English physicist, mathematician, astronomer and natural scientist who lived between 1643-1727 Newtons the amount of force needed to move 1 kilogram of an object 1 meter per second squared Nilometer a device used to measure the flooding on the Nile River. Nonlinear systems a system that does not add up to all of its parts, Null hypothesis in statistics, a null hypothesis is a hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. When used, the null hypothesis is presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. In classical science, the null hypothesis is used to test differences in treatment and control groups, and the assumption at the outset of the experiment is that no difference exists between the two groups for the variable being compared Number line a number line is a one-dimensional picture in which the integers are shown as specially-marked points evenly spaced on a line. Although this image only shows the integers from -9 to 9, the line includes all real numbers, continuing "forever" in each direction. It is often used as an aid in teaching simple addition or subtraction, especially involving negative numbers. Number theory the study of the properties of numbers Number is a quantity associated with a symbol Numeral the symbol for a number Numerator the part of a fraction above the line, the number to be divided

O

 Obtuse triangle a triangle with one internal angle larger than 90° (an obtuse angle). Octahedron a three dimensional shape made with 8 triangles Ordinal numbers a number that says where an item is ordered in a group (such as days of a month) Ordinate the y-coordinate of a point: its distance from the x-axis measured parallel to the y-axis. Origin the center of a graph. (0,0) are the coordinates used to represent the distance on the x-axis and the y-axis. Orthorhombic in crystallography, three unequal axes all at right angles to each Ounces 1/16 of a pound

P

 Pacioli,  Luca an Italian mathematician and Franciscan friar, collaborator with Leonardo da Vinci, and seminal contributor to the field now known as accounting. His work on Divina Proportions captured the imagination of mathematicians, artists, architects, scientists, and mystics. Pattern repeating design Pentagon a five-sided polygon Pentagonal symmetry the division of an object into five roughly equal parts Pentagram the shape of a five-pointed star drawn with five straight strokes. Percentage a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). Perimeter the length of the outside of a circle or shape Perpendicular at right angles Perpendicular vertical; straight up and down; upright. In Geometry perpendicular means meeting a given line or surface at right angles. Phi a mathematical constant ~ 1.6180339887 Pie graph A pie chart is a circular chart divided into sections, illustrating relative magnitudes or frequencies. Plane symmetry plane symmetry means a symmetry of a pattern in the Euclidean plane; that is, a transformation of the plane that carries lines to lines and preserves distances Plane a flat polygon Platonic solids three dimensional shapes that have equal sides, angles and face Polygon a two dimensional shape made with three or more sides Polyhedrons a three dimensional shape with four or more sides Positive numbers a number that is greater than zero. On a number line all positive numbers are always to the right. Pounds English system of measuring weight equal to 453.59237 grams Precise strictly following a pattern, standard or convention Prism a polyhedron with two or more faces in parallel planes Problem the question you have when doing a scientific experiment. Proof the reason a certain statement is true using known theorems. Properties characteristics that an object or thing has Proportion the equality of two ratios such as 4/2= 10/5 Protractor a tool, usually in the shape of a half circle, used to measure angles Pythagorean Theorem the formula used to find an unknown length of a right angled triangle, the two sides that meet to form the right angle equal to the long side connecting them.  a2 + b2 = c2

Q

 Quadrants any of the four areas into which a plane is divided by the reference axes in a Cartesian coordinate system, designated first, second, third, and fourth, counting counterclockwise from the area in which both coordinates are positive. Qualitative pertains to or is concerned with quality or qualities. Quantification the ability to give a value to an action or thing to better model it

R

 Radial symmetry the most symmetrical, no matter how you cut an object with radial symmetry it will divide it into equal images Radium a radioactive element, which has the symbol Ra and atomic number 88. Ratio the mathematical relationship between two or more numbers Rational a number that can be represented by a fraction or ratio Relative not absolute, related to something else Researchers scientists who study the effects of various things to expand our scientific knowledge Rhombohedral three dimensional parallelogram or rectangle Riemannian geometry as two seemingly parallel lines continue eventually they will meet Right triangle a right triangle has one 90° internal angle (a right angle). The side opposite to the right angle is the hypotenuse; it is the longest side in the right triangle. The other two sides are the legs of the triangle. Rotational symmetry an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry Ruler a straight edge with markings used to measure length Rules a regulating feature

S

 Scalene triangle a triangle with all sides of different lengths and angles Scientific method the techniques used to investigate phenomena and acquiring new knowledge, based on gathering observable and measurable evidence, subject to specific principles of reasoning. Six-fold symmetry the division of an object into six equivalent parts Slugs the mass unit in the English system ~ 32.17405 pound-mass Solid geometry looks at how three dimensional shapes interact with their sides Solid a state of matter when all atoms are arranged in a structured form Solutions a step in scientific method and means the answer to or disposition of a problem. Specific properties Specific properties of a substance are derived from other intrinsic and extrinsic properties; for example, the density of steel (a specific and intrinsic property) can be derived from measurements of the mass of a steel bar (an extrinsic property) divided by the volume of the bar (another extrinsic property) Spring constant in Hooke’s experiment the spring constant is the measure of stiffness multiplied by the distance the end of the spring moved. Statistics a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities. Statistics are also used for making informed decisions – and misused for other reasons – in all areas of business and government. Surface area the area of the outside of an object or the area contained in a shape Symbol a sign used in writing and printing to represent an action Symmetry the divisibility of an object after changing its perspective

T

 Temperature the measurement of the hotness or coldness of an object Tessellation a tessellation is a group of polygons that fills the plane with no overlaps and no gaps and is repeatable. Tetragonal in crystallography, the tetragonal crystal system is one of the 7 lattice point groups. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base and height Tetrahedron a shape formed by having four sides, all triangles Theorem a formula or statement that is proven by other formulas Three dimensional the measurement of something in three directions such as length width and height Three-fold symmetry the division of an object into three equivalent parts Tiling another term for tessellation, used when describing actual tiles or bricks and when describing periodic and aperiodic tiling. Time the period when events occur Trade the voluntary exchange of goods, services, or both. Trade is also called commerce. A mechanism that allows trade is called a market. The original form of trade was barter, the direct exchange of goods and services. Modern traders instead generally negotiate through a medium of exchange, such as money. Transformation change into something else Translation symmetry in physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation. Discrete translational symmetry is invariance under discrete (quantized) translation. Triclinic in crystallography, the triclinic crystal system is one of the 7 lattice point groups. A crystal system is described by three basis vectors. In the triclinic system, the crystal is described by vectors of unequal length, as in the orthorhombic system. Trigonometry the relationship between angles and sides and the formulas to find them Two dimensional the measurement of something in two directions such as length and width or latitude and longitude, flat looking

U

 Unit Cell the smallest building block of a crystal, consisting of atoms, ions, or molecules, whose geometric arrangement defines a crystal's characteristic symmetry and whose repetition in space produces a crystal lattice (an arrangement in space of isolated points in a regular pattern, showing the positions of atoms, molecules, or ions in the structure of a crystal.) Unit a given amount used for measurement (meter, liter, gram, pound)

V

 Vertex the point where two lines (in polygons) or three faces (in polyhedrons) meet and connect Volume the amount of space a three dimensional object takes up, measured in cubic meters or liters von Koch, Helge a Swedish mathematician who lived from 1870-1924 who modeled one of the best fractals known

W

 Weight the measurement of the effect of gravity on an object Wieman, Carl a Nobel-prize winning American physicist at the University of British Columbia who (with Eric Allen Cornell), in 1995, produced the first true Bose-Einstein condensate. Wieman joined the University of British Columbia physics faculty on January 1st, 2007 and is heading a well-endowed science education program there; he retains a 20% appointment at CU to head the science education project he founded in Colorado.

X

Y

Z

 Zenith the place directly above someone or thing in relation to the horizon