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The Math in Eye Glasses. Kate McCauley GED 613 Math Notebook.

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the math in eye glasses

The Math in Eye Glasses

Kate McCauley

GED 613

Math Notebook


Math in the World Around UsWhen deciding upon a subject for my math notebook, I chose an everyday item that I was familiar with-eyeglasses. Both my grandfather and father are optometrists and I spent a lot of time around glasses growing up. Upon taking a closer look, I was surprised to find so many examples of math around glasses. Here are some of those examples:

the history
The History
  • The first item resembling eyeglasses was the magnifying glass. It was invented around 1000 A.D
  • The Venetians developed glass reading stones which were placed directly on the page of a book
  • In the year 1268, an English philosopher by the name of Roger Bacon writes about using a cut piece of glass to better see “letters or other minute objects.



That’s 741 years ago!

the materials
The Materials
  • Glass

Pure silica has a "glass melting point“ of over 2300 °C (4200 °F). It can be made into glass, but other substances are added to simplify processing. One is sodium carbonate, which lowers the melting point to about 1500 °C (2700 °F) in soda-lime glass. The resulting glass contains about 70 to 74% silica by weight and is called a soda-lime glass. Soda-lime glasses account for about 90% of manufactured glass.

  • Metal

Metals have various melting points depending upon the type. A few examples are listed below:

Melting Point Degrees are in both Celsius and Fahrenheit

Aluminum 659 C 1218 F

Brass 900-940 C 1652-1724 F

Gold 1063 C 1946 F

Silver 961 C 1762 F

Stainless Steel 1363 C 2550 F

Titanium 1795 C 3263 FTo go from Fahrenheit to Celsius:

That’s HOT!1. Begin by subtracting 32 from the Fahrenheit number.

2. Divide the answer by 9.

3. Then multiply that answer by 5.

  • Plastic

Plastic is also a common material.

the parts
The Parts
  • Frame front: Front part of the eyeglass frame that holds the lenses in place and bridges the top of the nose.
  • Eye wires (rims): Part of the frame front into which the lenses are inserted.
  • Bridge: The area between the lenses that goes over the nose and supports
  • 90 % of the weight of the eyeglasses. There are many different types of bridges including keyhole, saddle and
  • End pieces: Extensions of the frame front to which the temples are attached.
  • Hinges: Part of the frame that connects the frame front to the temples and allows the temples to swing.
  • Temples: Parts of the frame that extend over and/or behind the ears to help hold the frame in place. There are many different types of temples including skull, comfort-cable, riding bow, spring-hinged and library. Skull is the most popular temple.

These parts are made with different lengths in order to fit a person’s face.

measurements all measured in mm
MeasurementsAll measured in mm
  • Papillary Distance (PD)- the distance between a person’s eyes (the center of one pupil to the other)
  • Segment (Seg) Height-the height which the bifocal is set measured from the bottom of the frame
  • Lens Circumference-the measured distance around the outside of the lens.
  • Frame Size- the distance from one side of the frame to the other corresponding side.
  • Temple Size- the length of the temples.
  • Bridge Size- the distance between the two eye wires.

So Many Lengths to Measure! It is important that each of these measurements are correct to create the pair of glasses that best fits you. If a child wears glasses, these lengths will change as the child grows. As stated on the previous slide, these lengths are measured in mmMy own measurements are listed below:arm length= 115mmbridge width= 17.5mmlens depth= 27.5mm

operation signs and vision
Operation Signs and Vision
  • + = far sighted person (convex)

Example +1.00 is one diopter of far sightedness.

  • - = near sighted person (concave)

Example -2.00 is two diopters of near sightedness

Diopter is the unit of measurement used to measure the concave or convex shape of the lens. This shape reflects light. More on diopters in the next slide!

diopter definition this was really hard to understand but important
Diopter DefinitionThis was really hard to understand but important!
  • The optical power of a lens with a focal length of 1 meter (about 39 inches) is said to be 1 diopter. Because the formula is based on the reciprocal of the focal length, a 2 diopter lens is not 2 meters but 1/2 meter, a 3 diopter lens is 1/3 meter and so forth. This is important because magnification increases as the focal length gets shorter, which is why a prescription for a higher diopter correction means you need more magnification.
  • The optical power of the

human eye is about 40 diopters.

the chart
The Chart
  • In 1862, a Dutch Ophthalmologist, Dr. Hermann Snellen, devised the eye chart. He determined that there was a relationship between the sizes of certain letters viewed at certain distances. The normal height for the letter E is

88 mm, and the viewing distance is 6 meters.

1 meter = 3.2808399 feet

6 meters = 19.6850394 ft

what is 20 20 vision
What is 20/20 Vision?
  • The Snellen fractions, 20/20, 20/30, etc., are measures of sharpness of sight. They relate to the ability to identify small letters with high contrast at a specified distance.
  • “Visual acuity is said to be 1/2 (or an equivalent fractional value, such as 20/40, 6/12, etc.). If the magnification needed is 5x, visual acuity is 1/5 (20/100, 6/30, etc.), and

so on.” (Dr. August Colenbrander)

the best shape
The Best Shape
  • Eyeglass frames and faces come in many shapes. Certain shapes compliment each other. Choosing a frame that compliments your face is part of what makes one pair of glasses look better than another.

Geometry includes shapes and their corresponding angles. The next two slides will show display these angles.

  • The length of the bridge and width of the frame are important factors to consider when picking out the best frame.
  • Colors are too!
  • Quadrilateral

Any shape with four sides including rectangles and squares

  • Rectangle

A four-sided polygon having all right angles. The sum of the angles of a rectangle is 360 degrees.


  • Square

A four-sided polygon having equal-length sides meeting at right angles. The sum of the angles of a square is 360 degrees.


  • For Fun!

Some frames are triangular. There are two triangles in every square!


Shapes continued…OvalThe area of an oval is given by: Pi x 0.5a x 0.5b (Pi is the ratio of a circle's circumference divided by its diameter )Where a is the length of the longest side at its greatest width, and b is the length of the shortest side at its greatest height.CircleA circle's circumference or perimeter is the distance around the circle. The diameter is the line length from one point on the circle to the opposite point on the other side. The line goes through the center of the circle and ends on the circle.The Radius of a circle is the distance from the center of the circle to the outside edge.


SunglassesSunglasses areimportant for multiplereasons. They include1. uv protection2. glare protection3. eliminating certain frequencies of lightSunglasses can be made to block varyingpercentagesof uv light. You can get sunglassthat block 100% !


ConclusionIt is amazing that math can be related toso many things in the world. After all, it is logic and pattern. Thank you for learning a little about how math relates to eyeglasses-an object that many of us wear everyday!