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How to tie the shortest shoelace

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TANJONG KATONG GIRLS' SCHOOL. Cho Soo Min (Secondary 2E7 / 3E8) ... Straight European Method. Length used = 5h 2d 4(h2 4v2 )(Pythagoras' Theorem) ... – PowerPoint PPT presentation

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Title: How to tie the shortest shoelace


1
  • How to tie the shortest shoelace?

TANJONG KATONG GIRLS SCHOOL Cho Soo Min
(Secondary 2E7 / 3E8) Tay Wen Niang Sheryl
(Secondary 2E7 / 3E8) Kwok Wai Sze (Secondary 2E7
/ 3E9)
2
Aim
  • To find various lacing methods that are commonly
    used by people
  • To find the shortest lacing method

3
Literature Review
  • Criss-cross, or the bow-tie? There were
    different opinions.
  • It turns out, however, that shorter lacings are
    possible if the lace doesn't have to pass
    alternately through the eyelets on the left and
    right side of the shoe.

4
Criteria
  • We found out the minimum criteria for a
    safe-to-use method.
  • The shoelace must go through all the holes of the
    shoe.
  • The shoelace need to go from one side to the
    other at least for five times.

5
  • Before showing the lacing methods, here are some
    of the points to be taken note of
  • Regard the thickness of the shoelace be 0 cm
  • There will not be any twisting of the shoelace
  • Consider the length used to tie the knot would be
    same for all the methods.

6
  • Let the distance between the holes be

7
Methodology
  • Use algorithms to find the shortest lacing
    method.
  • Form a formula for each lacing methods and
    substitute numbers.
  • Create a shorter lacing method if possible

8
a) Algorithms
  • What is algorithm?
  • An algorithm is a specific set of instructions
    for carrying out a procedure or solving a
    problem, usually with the requirement that the
    procedure terminate at some point.
  • There are many types of algorithms, and some of
    them can be used to find the shortest route in a
    specified area.
  • Finding shortest lacing method could be regarded
    as a limited version of salesman problem, where
    we have to find the shortest route (in this case,
    lacing method). Thus, we went on investigating
    different algorithms that could suit our project.

9
a) Algorithms
10
Remarks
  • After judging each of the algorithms, we realized
    that none of them suits our project, as they will
    produce a route (in this case, lacing method)
    that does not suit our criteria - not going from
    one side to the other at least for five times.

11
b) Form a formula for each lacing methods and
substitute numbers.
First of all, we chose the model shoe so that we
can substitute in the numbers.
Figure 1.1 The model shoe
12
Straight European Method
Length used 5h 2d 4(vh2 4v2
)(Pythagoras Theorem) 5 x 5 2 x 5.3852 4 x
6.4031 61.4 cm (3 s.f.)
13
Lattice Lacing
Length used h 4v 6 (vh2 9v2 )(Pythagoras
Theorem) 1 x 5 4 x 2 6 x 7.8102 59.9 cm
(3 s.f.)
14
Sawtooth Lacing
Length used 5h 2v 4(vh2 4v2 )(Pythagoras
Theorem) 5 x 5 2 x 2 4 x 6.4031 54.6 cm
(3s.f.)
15
Which method uses the least amount of shoelace?
16
Substituting different measurementsLet h 4
cm, v 1.5 cm, d v42 1.52(Pythagoras)
4.2720 cm (5 s.f.)
17
Substituting different measurementsLet h 6
cm, v 2 cm, d v62 22(Pythagoras) 6.3246
cm (5 s.f.)
18
Substituting different measurementsLet h 5
cm, v 1.5 cm, d v52 1.52(Pythagoras)
5.2202 cm (5 s.f.)
19
Substituting different measurementsLet h 5.5
cm, v 2 cm, d v5.52 22(Pythagoras)
5.8523 cm (5 s.f.)
20
Substituting different measurementsLet h 4
cm, v 1 cm, d v42 12(Pythagoras) 4.1231
cm (5 s.f.)
21
Result analysis
  • For all our results, the bow-tie method was still
    the shortest method. Thus, it is safe to say that
    the bow-tie method is more or less the shortest
    lacing method.
  • However, as some of the results changed, one
    should know the dimensions of the shoe before
    working out the formulae to find the shortest
    method as the result might vary.

22
c) Create a shorter lacing method
  • Is it possible to create a shorter lacing method?
  • So far, we have found that the bow-tie method is
    the shortest lacing method.

Thus, we would have to first see if we Can
minimize the length used in the bow-tie Method.
23
Is it possible to minimize the length used by
the bow-tie method?
  • Properties of bow-tie method
  • Bow-tie method goes through all the holes.
  • It goes from one side to the other for exactly 5
    times without overlapping even once.

Bow-tie method
24
Is it possible to minimize the length used by
the bow-tie method?
Figure 1. Bow-tie method
Figure 2. Shortened Bow-tie method
25
Conclusion
  • The length of the shoelace differs very much
    depending on which lacing method you are using,
    and the shoe shop method, which many shoe shops
    are using because it is regarded as the fastest
    way, actually is one of the longest lacing
    methods.

26
The shortest lacing method is the bow-tie method
no matter what size of the shoe is.
27
Recommendation
  • one should use the bow-tie method if he / she
  • has limited length of shoelace
  • wants to shorten the shoelace to
  • save the material

28
dress with ribbons- joining two materials
together by punching holes and tying -
packaging and tying (help the factories in
packaging their products and cutting down on
their costs, especially since the current
Economic crisis.
Application
29
Reference
  • Ian W. Fieggen (2003 2008)
  • Ivars Peterson (1999)
  • Burkard Polster (2006)
  • Burkard Polser (2002) Nature What is the best
    way to tie shoelace? (Dec 2002 Nature)
  • RANDY LEWIS (1986) Search for Perfect Shoelace
    Ties Him Up
  • HOLLIS W FIELD (1910) One Reason Why Men Go
    Insane Shoe Laces Made Extra Short.
  • Curet, William D. (2007)
  • Smith, Gregory S. (2007)
  • James M. Parks Solving Geometry Problems in
    Everyday Life
  • Wonder-how-to www.wonderhowto.com
  • Ivars Peterson (2002) Five-Suit Decks,
    Traffic-Jam Puzzles, and Other Treats
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