fundamental group
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enMaths in a minute: The fundamental group
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<div class="field field-name-field-abs-txt field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><p>Topologists famously think that a doughnut is the same as a coffee cup because one can be deformed into the other without tearing or cutting. In other words, topology doesn't care about exact measurements of quantities like lengths, angles and areas. Instead, it looks only at the overall shape of an object, considering two objects to be the same as long as you can morph one into the other without breaking it. But how do you work with such a slippery concept? One useful tool is what's called the fundamental group of a shape.</p>
</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Topologists famously think that a doughnut is the same as a coffee cup because one can be deformed into the other without tearing or cutting. In other words, topology doesn't care about exact measurements of quantities like lengths, angles and areas. Instead, it looks only at the overall shape of an object, considering two objects to be the same as long as you can morph one into the other without breaking it. But how do you work with such a slippery concept?</p></div></div></div><div class="field field-name-taxonomy-vocabulary-1 field-type-taxonomy-term-reference field-label-above"><div class="field-label">tags: </div><div class="field-items"><div class="field-item even"><a href="/content/tags/topology">topology</a></div><div class="field-item odd"><a href="/content/tags/group-theory">group theory</a></div><div class="field-item even"><a href="/content/category/tags/fundamental-group">fundamental group</a></div><div class="field-item odd"><a href="/content/category/tags/maths-minute">Maths in a minute</a></div></div></div>Mon, 11 Apr 2011 09:18:34 +0000mf3445465 at https://plus.maths.org/content