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Calendar of Assignments

Page history last edited by Jonathan Dietz 6 years, 5 months ago

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Date
Assignment Due (to be done before class starts on date listed at left) Readings  Videos 
 
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9/5  

Introduction to Euclid as the Father of Geometry

 ( Video)

 

HW: 

Active Geometry: The House that Euclid Built

  

 

9/6 

 In geometry, Thales' theorem (named after Thales of Miletus) states that if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ABC is a right angle. Thales' theorem is a special case of the inscribed angle theorem. It is generally attributed to Thales, who is said to have sacrificed an ox in honor of the discovery, but sometimes it is attributed to Pythagoras.

Khan Academy: Euclid as the Father of Geometry

 

Lincoln(2012)-Euclid Quote

 

Euclid and Politics

 

 

 

 
 

 

   

Carl Sagan Cosmos- Eratosthenes

 

Theta= 1/50 of 360 degrees

 

10 stade= 1 mile

 

 

http://www.wired.com/science/discoveries/news/2008/06/dayintech_0619

 

Carl Sagan on the death of Hypatia of Alexandria

   
 

History Connection: Was Columbus a Great Navigator? 

 

Catigara is also shown at this location on Martin Waldseemueller’s 1507 world map, which avowedly followed the tradition of Ptolemy.[11] Ptolemy’s information was thereby misinterpreted so that the coast of China, which should have been represented as part of the coast of eastern Asia, was falsely made to represent an eastern shore of the Indian Ocean. As a result, Ptolemy implied more land east of the 180th meridian and an ocean beyond. Marco Polo’s account of his travels in eastern Asia described lands and seaports on an eastern ocean apparently unknown to Ptolemy. Marco Polo’s narrative authorized the extensive additions to the Ptolemaic map shown on the 1492 globe of Martin Behaim. The fact that Ptolemy did not represent an eastern coast of Asia made it admissible for Behaim to extend that continent far to the east. Behaim’s globe placed Marco Polo’s Mangi and Cathay east of Ptolemy’s 180th meridian, and the Great Khan’s capital, Cambaluc (near Beijing), on the 41st parallel of latitude at approximately 233 degrees East. Behaim allowed 60 degrees beyond Ptolemy’s 180 degrees for the mainland of Asia and 30 degrees more to the east coast of Cipangu (Japan). Cipangu and the mainland of Asia were thus placed only 90 and 120 degrees, respectively, west of the Canary Islands.

 

 

Christopher Columbus modified this geography further by using 53⅔ Italian nautical miles as the length of a degree instead of the longer degree of Ptolemy, and by adopting Marinus of Tyre’s longitude of 225 degrees for the east coast of the Magnus Sinus. This resulted in a considerable eastward advancement of the longitudes given by Martin Behaim and other contemporaries of Columbus. By some process Columbus reasoned that the longitudes of eastern Asia and Cipangu respectively were about 270 and 300 degrees east, or 90 and 60 degrees west of the Canary Islands. He said that he had sailed 1100 leagues from the Canaries when he found Cuba in 1492. This was approximately where he thought the coast of eastern Asia would be found. On this basis of calculation he identified Hispaniola with Cipangu, which he had expected to find on the outward voyage at a distance of about 700 leagues from the Canaries. His later voyages resulted in further exploration of Cuba and in the discovery of South and Central America. At first South America, the Mundus Novus (New World) was considered to be a great island of continental proportions; but as a result of his fourth voyage, it was apparently considered to be identical with the great Upper India peninsula (India Superior) represented by Behaim—the Cape of Cattigara. This seems to be the best interpretation of the sketch map made by Alessandro Zorzi on the advice of Bartholomew Columbus (Christopher’s brother) around 1506, which bears an inscription saying that according to the ancient geographer Marinus of Tyre and Christopher Columbus the distance from Cape St Vincent on the coast of Portugal to Cattigara on the peninsula of India Superior was 225 degrees, while according to Ptolemy the same distance was 180 degrees.[12]

   
  Review Week #1     
 

Introduction to SketchUp 

 

 

Assignment:

 

  •  Design Small house or structure
  • Structure should be solid model
  • Scale Model to < 1" in size 
  • Assemble models as a group 
  • Export as STL file 
  • Save 
   
 

Introduction to 3-D Printing 

 

  • Download and install BFB Axon 2 Software (PC only, sorry)
  • Open STL file, scale, set build parameters, "build", save build file as BFB file per Axon2 Manual
  • Setup Rapman 3.2 printer per Rapman manual
  • Insert build file into printer, hit 'print'

 

 

  

Tutorials:

 

Design a small house and small furniture item, and fabricate on 3-D printer 

 

   
   

Introduction to Art of Problem Solving-Geometry

 

Geogebra- Geometry Software

 

Optional--Khan Academy Intro to Geometry (take notes)

 

 

Richard Feynman on youtube on beauty

 

Opening Scene of "Infinity"

Feynman Diagrams 

 

Video Example: Two Column Proof

 

Latex for Geometry Proof

 

Reading: Chapter 1, Sections 2.1-2.5

 

Do notes and  exercises

 
 
9/24 

Art of Problem Solving Introduction to Geometry Begins

 

  •  Week 1: Angles
    • Points, lines, rays, segments, planes
    • Measuring angles
    • Parallel lines
    • Angles in a Triangle 

Sections 2.6-2.7, 3.1-3.5

 
10/1 
  •  Week 2: Congruent Triangles
    • Exterior angles
    • Congruent Triangles-SSS, SAS, Funky Triangles  

 

 

 

Sections 2.6-2.7, 3.1-3.5

Khan Academy: Triangles 
10/2 

Enrichment: Visit from Henry Skupniewicz, MIT Department of Architecture

 

 

 

http://henryskup.com/ 

 Arranged by Jeanette Nip- Science PTO

 

   
10/5

Enrichment: Mathemusician Vi Hart

 

Computational Origami

 

 

 

 

 

 

 

 

   
10/8 
  •  Week 3: Area
    • Isoceles and Equilateral triangles 
    • Perimeter and Area 
Section 3.6-3.7, Chapter 4  
10/15 
  •  Week 4: Similar Triangles
    • What is Similarity?
    • Types of Similarity-AA, SAS, SSS
    • Construction techniques  

 

Chapter 5  
10/22  Chapter 5, Sections 6.1-6.2   
10/29  Sections 6.3-6.6   
 

 

 

 

 

 

 

 

 

 

 

 

Origami with Catherine Zhao 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Catherine's Slide Show of Work

 

Links:

 

 

Math for Halloween:

 

 

   
11/5 
  •  Week 7: Special Parts of a Triangle
    • Bisectors
    • Perpendicular Bisectors
    • Angle Bisectors
    • Medians 

 

 

Compass Constructions 

Geometry of Gothic Architecture

Sections 7.1-7.4   
11/12 
  •  Week 8: Special Parts of a Triangle
    • Altitudes
    • Constructing Bisectors 

 

Leonhard Euler 

 

 

Video: Between the Folds

 

 

 

 

Food for Thought: A Mathematical Thanksgiving Feast

 

------------------------------------------------------------------------------------------

 

Mathematical Science Fiction:

 

 

Mathematical Songs:

 

Sections 7.5-7.7   
11/26 

 

  • Week 9: Quadrilaterals 
    • Quadrilateral Basics
    • Trapezoids
    • Parallelograms 

 

  • The median is parallel to the bases and its length is the average of the lengths of the bases.
  •  The area of a trapezoid equals the product of the length of the median and the distance between the two parallel sides (which we call the height).
  •  If the angles of a trapezoid along the same base are equal, then the trapezoid is an isosceles trapezoid. In an isosceles trapezoid, the legs are equal in length, as are the diagonals
  •   two general strategies that are useful in trapezoid problems: (1) use what we know about parallel lines and similarity, and (2) drop altitudes to form right triangles.
  • A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel (hence the name).
  • In a parallelogram, opposite sides are equal in length and opposite angles are equal in measure. Also, the diagonals of a parallelogram bisect each other.
  • The area of a parallelogram equals the product of a side length and the height from that side to the opposite side.
  • A rectangle is a quadrilateral with all equal angles. Rectangles are parallelograms, inheriting all of those properties. They additionally have equal diagonals.
  • A rhombus is a quadrilateral with all equal sides. Rhombi are also parallelograms, and their diagonals are perpendicular.
  • The area of a rhombus, or in fact any quadrilateral with perpendicular diagonals, is half the product of the diagonals.

 

 

Field Trip to MIT 

 

 

 

Meeting with Marty and Erik Demaine

 

 

Humanoid Robot PR2: 

 

Video of PR2 Baking a Cake

 

 

SEG Origami Robot:( see http://people.csail.mit.edu/cagdas/SEG/SEG__MITs_Origami_Inspired_Submission.html )

 

 

LegoNxT Finite State Machine Presentation- Lindsay Sanneman and Dylan Hadfield, MIT  PowerPoint

 

LegoNxT Program, Road Clearing

Sections 8.1-8.3   
12/3 

  

Geometry of Soap Bubbles

 

 

Note 120 degree angles

 

Geometry of Soap Bubbles

 

Exploratorium: When Bubbles Meet Bubbles

 

The Shape of Bubbles

 

 

Regardless of their relative sizes, the bubbles will meet the common wall at an angle of 120 degrees. This is easy to see in the bubble picture to the right. All three bubbles meet at the center at an angle of 120 degrees. Although the mathematics to prove this are beyond the scope of this article, the 120 degree rule always holds, even with complex bubble collections like a foam. 

 

 

 

 

 

 

Bubble Colors

 

"...If the crests of two or more waves are in step (yellow and magenta waves top), or almost in step, they can combine into a larger or more intense effect (red wave top.) This is called "constructive interference." If the crest of one wave meets the valley of another (yellow and magenta waves bottom), they cancel each other out (red wave bottom.) When two light waves cancel each other, the result is darkness and this is called "destructive interference."   

 
  • Week 10: Quadrilaterals 
    •  Rhombi
    • Rectangles
    • Squares 
    • If and Only If 

 

 

Sections 8.4-8.8   

 

 

Music and Mathematics:

 

 

Vi Hart at Gel 2011 from Gel Conference on Vimeo.

 

Vi Hart Videos on Mathematics and Music:

 

 


    

 

 

 

 

 

ZOME EXPLORATIONS 

 

 


 

  • the shortest distance from a point outside a circle to the circle is along the segment connecting the point to the center of the circle.  
  •  the sum of the interior angles of a polygon with n sides is 180(n-2) degrees, and
    • the sum of the exterior angles of a polygon is 360 degrees.
    • A regular polygon has all its sides equal and all its angles equal.
    • the measure of each interior angle of a regular polygon is 180(n-2)/n and the measure of each exterior angle is 360/n.
    • a polygon with n sides has n(n-3)/2 diagonals.
    • the area of a regular polygon equals half the product of the perimeter of the polygon and the distance from the center of the polygon to one of the sides of the polygon. (This distance is called the apothem.) 
Chapter 9   
12/17 

 

Vi Hart: Snowflakes, Starflakes, and Swirlflakes

 

Vi Hart: Gauss Christmath Special

Chapter 10   
1/7 

Vi Hart: Dialogue for 2

 

 

Gothic Geometry- Rose Window

 

 

 

  • Week 13: Circles and Funky Areas 
    • Arc Measure, Length, and Circumference
    • Area
    • Funky Areas  
Chapter 11   
1/14 
  • Week 14: Circles and Angles 
    • Inscribed Angles
    • Angles Inside and Outside Circles  

 

RIP Aaron Swartz 

War for the Web - Excerpts from Aaron Swartz interview, July 10, 2012 from War for the Web on Vimeo.

 

Vi Hart- Spherical Snowflakes

 

Snowflake Gallery

 


Sections 12.1-12.2   
1/21 

 

 

 

Alternate Segment Theorem 

Sections 12.3-12.5   
1/28 

 

Week 16: Power of a Point  

 

 

 

See also: http://www.regentsprep.org/Regents/math/geometry/GP14/PowerTheorem.htm

 

Google Science Fair

 

Pizza Physics

Chapter 13 

Khan Academy: Vision

 

Vi Hart's Guide to Comments

 

MIT Admissions Director at Maker Faire

How to Get Into MIT

 

MakerFaire

 

 

2/4 

 

 

Chapter 14 

Paper Polyhedra 

 

Live-in Polyhedra

 

Vi Hart-Fruit Polyhedra

 

Soda Straw Tensegrity Structures

 

Pumpkin Polyhedra

2/11 
  • Week 18: 3-D Curved Surfaces 
    • Cylinders
    • Cones
    • Spheres 
Chapter 15   
2/18 
  • Week 19: Transformations  
    • Translations
    • Rotations
    • Reflections
    • Dilations
    • Transformations 
Chapter 16   
2/25 
  • Week 20: Coordinate Geometry I 

 

DesCartes and the Fly 

 

 

Week 20 Proof 10:

 

 

Sections 17.1-17.3, 17.5   
3/4 
  • Week 21: Coordinate Geometry II 
    • Proofs
    • Advanced analytic Geometry Problems  

 

DesCartes and the Fly

 


Sections 17.4, 17.6   
3/11 
  • Week 22: Introduction to Trigonometry 
    • Trigonometry and Right Triangles
    • Not just for right triangles
    • Law of Sines and Cosines  

 

 

 

 

 

Rocket Flight Equations( NASA):  http://exploration.grc.nasa.gov/education/rocket/rktpow.html

http://exploration.grc.nasa.gov/education/rocket/flteqs.html

 

Initial Mass of Rocket: 22 grams

Weight of Fuel: 6.24 gm

Average Thrust= 6 Newtons

Burn Time: 0.8 seconds

Apogee reached: Approx 3.5 seconds

Estimated Height: 70 meters

 

 Pi Day 2013

 

Pi Day.org

 

Pi Day 2013 at the Exploratorium

 

Vi Hart: Pi is Still Wrong 

Chapter 18   
3/18 
  • Week  23: Problem-Solving Strategies in Geometry  
    • The Extra Line
    • Assigning Variables
    • Proofs  

 

 

Chapter 19   
3/25 
  • Week 24: More Problem-Solving Strategies in Geometry 

 

 

 

Honors Geometry Review Problems

 

 

Celebrating the Completion of the AOPS geometry course!

 

Chapter 19   
 

GROUP THEORY 

 

Textbook on Groups-Part I

 

 

 

 

 

 

 

 Art of Problem Solving Outline of Group Theory

   
 

 

 

 

  •  
  •  
   
 

 

   
 

 

 

Professor Javed Aslam introduces students to binary arithmetic for computing.

 

Math Aside: Binary Arithmetic

  

Discrete Math Aside May 2nd-

 

Notes on Transistors and Logic Gates

 

Boolean Algebra

 

DeMorgan's Theorem

  

May 17th- Algorithms

 

   
 

 

Introduction to Arduino and Physical Computing 

   
 

 

Why are we doing this?

 

 

 

 

 


 

Software:

 

  • Arduino Software:  http://www.arduino.cc/  - Go to "Download"; download Arduino IDE Folder; Follow Instructions under "Getting Started"
  • Fritzing ( Circuit Design Software):  http://fritzing.org/ - Go to "Download"

 

 


Hardware:

 

 


 Math Aside:

 

 

Notes- Number Representations 

 


Texts:

 


 

1. Basic Circuit Theory

 

 

 


 

 

Examples of Arduino Circuits 


2. Schematics 

 


3. Introduction to Arduino : Blink

 http://www.youtube.com/watch?v=xKwox3dd-dE&feature=share&list=PL8CD32146ED5CD04E  (2:30)

 

Also:Intro to Arduino http://youtu.be/pMV2isNm8JU

 

 

  •  Challenge 2: Make row of blinking LEDs-see answer

4. Sensors 1: Analog Read Serial- Reading an analog voltage, displaying it on the Serial Monitor 

 

 

 




Discrete Math Aside May 2nd-

 

Notes on Transistors and Logic Gates

Boolean Algebra

DeMorgan's Theorem

 

  


Introduction to Breadboarding:  http://www.youtube.com/watch?v=CssOBb-qaX0&feature=share&list=PL8CD32146ED5CD04E 

  


Sensors: 

Challenge 4: Read a Button : If/Else

http://www.mon-club-elec.fr/pmwiki_mon_club_elec/pmwiki.php?n=MAIN.ArduinoInitiationBPAppuiBpLedMinuteur

Reading: Arduino in a Nutshell pp. 9-10

 

 

 

 


 

 

 

Arduino-Bot: Video

 

Challenge: Build a robotic vehicle that can follow a wall at a fixed distance.

               

                    Add lights and buzzers that indicate if it is turning left, right, or going straight.

 

                    Add a servo motor that enables robot to scan left and right, and find its way

                    through a maze- see Explorer Bot

 

Example Code


Controlling Motors with an H-Bridge:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Creating Functions (useful for organizing code) 

 

Adjusting Output Speed with Pulse-width Modulation(PWM)

 

  analogWrite(pin,  value 0-255);

 

 

Sensors: 

Challenge 5: Control Tone with  Light Sensor

 


Challenge 6: Using Ultrasound

 

 

Challenge 7: Using Motors

 


 


 


Projects:

Software:

 

  • Arduino Software: http://www.arduino.cc/ - Go to "Download"; download Arduino IDE Folder; Follow Instructions under "Getting Started"
  • Fritzing ( Circuit Design Software): http://fritzing.org/ - Go to "Download"

 

   
 

Geometry Review:

 

  

 

  

 

   
 

Bonus Project :Sea Perch:

 

 

MIT Sea Grant's new SeaPerch program introduces pre-college students to the

 wonders of underwater robotics. Part of the Office of Naval Research's initiative,

"Recruiting the Next Generation of Naval Architects," this program teaches students

 how to build an underwater robot (called a SeaPerch), how to build a propulsion system,

how to develop a controller, and how to investigate weight and buoyancy. This endeavor

is one of many exciting new projects funded by the Office of Naval Research as part of its

National Naval Responsibility Initiative. The initiative focuses on bringing academia,

government and industry to work together to ensure that the talent needed to design

 the Navy's next generation of ships and submarines will be there when needed.

 

MIT Sea Perch http://seaperch.mit.edu/

 

Videos: Building the Sea Perch http://www.phillyseaperch.org/construction-videos.html

 

 

 

   
       
   

 

 

   

 

 

 

Salman Khan, of Khan Academy, interviewed by Rafael Reif, president of MIT

 

 

 

Civil Engineering students at MIT display model bridges utilizing Catenary Arches , which are self-supporting

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Surveyor using triangulation

to map locations

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