# Crochet and Hyperbolic Geometry

Interesting topic. These three books might be worth buying. The concept combines crochet, math, art, and nature.

https://en.wikipedia.org/wiki/Hyperbolic_geometry

Crocheting Adventures with Hyperbolic Planes http://www.amazon.com/Crocheting-Adventures-Hyperbolic-Planes-Taimina/dp/1568814526

https://en.wikipedia.org/wiki/Daina_Taimina

Taimina's way of exploring hyperbolic space via crochet and connections with nature, combatting math phobia ...

Crocheting Hyperbolic Planes: Daina Taimiņa at TEDxRiga

https://www.youtube.com/watch?v=w1TBZhd-sN0

https://mathandfiber.wordpress.com/2012/03/19/introduction-to-crocheting-hyperbolic-planes/

https://en.wikipedia.org/wiki/Mathematics_and_fiber_arts

http://www.amazon.com/Field-Guide-Hyperbolic-Space-Intersection/dp/0977962210

http://www.ted.com/speakers/margaret_wertheim

http://www.ted.com/talks/margaret_wertheim_crochets_the_coral_reef

https://www.guernicamag.com/interviews/at-home-in-the-universe/

http://crochetcoralreef.org/index.php

http://crochetcoralreef.org/order-crochet-coral-reef-book.php

http://www.math.cornell.edu/~henderson/books/eg00/

http://theiff.org/press/interweave.html

http://theiff.org/oexhibits/oe1.html

How to Crochet Hyperbolic Shapes

https://www.youtube.com/watch?v=iz3t7YrCjxM

The Complete Hyperbolic Crochet Video - Pseudosphere

https://www.youtube.com/watch?v=EZ2Fw-mS8c0

YouTube: Hyperbolic Geometry within the dynamics of space and time

http://proactive-art.org/post/26377191103/hyperbolic-crochet-coral-reef

http://www.cabinetmagazine.org/issues/16/crocheting.php

http://www.math.cornell.edu/~dwh/papers/crochet/crochet.html

http://www.mnh.si.edu/exhibits/hreef/

http://hyperbolic-crochet.blogspot.com/2011/05/geometric-manifolds-for-hyperbolic.html

http://www.d.umn.edu/cs/thesis/kedar_bhumkar_ms.pdf

http://asymptotia.com/2007/01/01/hooking-up-manifolds/

http://asymptotia.com/2006/09/21/go-figure/

http://homepage.ntlworld.com/crispin.roche/klein.txt ????????

http://members.tripod.com/professor_tom/hyperbolic/

http://hyperbolic-crochet.blogspot.com/2015/01/my-fiber-year-2014.html

http://www.cooperhewitt.org/2013/03/13/learning-by-crocheting/

http://blog.ted.com/crocheting_in_h/

- euclidean space
- a point
- a line
- parallel line: one line can run through the point and never touch the other line

- spherical space
- within a circle
- a point
- a straight line (curved on a sphere)
- how many straight lines can be drawn through the point that never meet the original line. answer = 0.
- on a sphere, the straight line (geodesic) is the biggest line that can be drawn: equator or lines of longitude.

- hyperbolic space
- straight line
- a point that contains an infinite number of "curved" lines that run through the point and never meet the original straight line. they appear curved on a flat surface (2 dimensional)
- non-euclidean geometry and general relativity
- https://en.wikipedia.org/wiki/General_relativity
- https://en.wikipedia.org/wiki/Non-Euclidean_geometry

## My Little Projects

October 2015:

- project one:
- chained six.
- used single crochet.
- crocheted two stitches in each stitch.
- at the end of each row, i think that i chained one, turned, and then two stitches in each stitch.
- crocheted four or five rows after the chain row.

- project two:
- chained four.
- slip-stitched into first stitch to make circle.
- used single crochet.
- six stitches into the ring.
- then crocheted 12 additional rows, spiraling around with the following pattern:
- one stitch, one stitch, two stitches into the previous row. is this a 1-1-2 ?

The small one is Project 1.

Another photo of Project 2.

August 2016 - Good way to use of inexpensive yarn. This uses the project 2 pattern above. It starts out slowly, but then it curls in on itself significantly.